Problem 45761. Sum of terms in a series 1 (★★★)

Created by Anirban Pal

Solve Later

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 191.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 95.65px; transform-origin: 407px 95.65px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 131.525px 10.5px; transform-origin: 131.525px 10.5px; unicode-bidi: normal; "><span style="">Given x and n, compute the following sum:</span></span></div><div style="block-size: 26px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 13px; text-align: left; transform-origin: 384px 13px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/gif;base64,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" data-image-state="image-loaded"></div><div style="block-size: 24px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12px; text-align: left; transform-origin: 384px 12px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.9833px 10.5px; transform-origin: 18.9833px 10.5px; unicode-bidi: normal; "><span style="">where</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 10.5px; transform-origin: 1.95px 10.5px; unicode-bidi: normal; "><span style=""> </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8.4px 10.5px; transform-origin: 8.4px 10.5px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; perspective-origin: 8.4px 8.5px; transform-origin: 8.4px 8.5px; ">|x</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 291.358px 10.5px; transform-origin: 291.358px 10.5px; unicode-bidi: normal; "><span style="">| indicates the absolute value of x. Thus, if x = -5 and n = 3, then the sum is (up to n = 3 terms)</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 109.633px 8.5px; transform-origin: 109.633px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">|-5|+|-5|^(1/2)+|-5|^(1/3)</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80.1167px 8.5px; transform-origin: 80.1167px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">= 5+5^(1/2)+5^(1/3)</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 29.5167px 8.5px; transform-origin: 29.5167px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">= 8.946</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4167px 10.5px; transform-origin: 84.4167px 10.5px; unicode-bidi: normal; "><span style="">Avoid using for/while loops.</span></span></div></div></div>

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Problem 45761. Sum of terms in a series 1 (★★★)

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