Problem 46873. Sum of terms in a series 2 (★★★)

Created by Anirban Pal

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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: 165.367px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.6833px; transform-origin: 407px 82.6833px; 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: 132.5px 8px; transform-origin: 132.5px 8px; unicode-bidi: normal; "><span style="">Given x and n, compute the following sum:</span></span></div><div style="block-size: 23.5px; 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 11.75px; text-align: left; transform-origin: 384px 11.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 294px;height: 18px" src="data:image/gif;base64,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" data-image-state="image-loaded" width="294" height="18"></div><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: 191px 8px; transform-origin: 191px 8px; unicode-bidi: normal; "><span style="">Thus, if x = 0.1 and n = 5, then the sum is (up to n = 5 terms)</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 40.8667px; 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 20.4333px; transform-origin: 404px 20.4333px; 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: 180px 8.5px; transform-origin: 180px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">0.1+2*(0.01)+3*(0.001)+4*(0.0001)+5*(0.00001)</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: 36px 8.5px; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">= 0.12345</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: 85.5px 8px; transform-origin: 85.5px 8px; unicode-bidi: normal; "><span style="">Avoid using for/while loops.</span></span></div></div></div>

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75 Solutions
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Last Solution submitted on Sep 24, 2021

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Rafael S.T. Vieira on 18 Oct 2020

Please, do not use isqual with floats, instead use abs(x1-x2) < 1e-10 for instance. A number like 0.1 is infinite and periodic in base 2.

goc3 on 27 Oct 2020

The test suite is updated to use a tolerance check.

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Problem 46873. Sum of terms in a series 2 (★★★)

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Problem 46873. Sum of terms in a series 2 (★★★)

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Last 200 Solutions

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