how to solve a equation involving summation from 2->infinity using matlab ? Require this regarding harmonic anlysis

Answer 1

[Walter Roberson]

Does omega(k)^6 strict increase faster than Vh(k)^2 increases? If it does then the summation converges (there may be other convergent situations as well.) In the case of convergence, you continue summing the terms with larger k until you detect that you have reached a situation where the rest of the sum is small enough that it could not affect the numeric value reached so far. (That is, the remaining sum is less than eps() of the current sum)

[sunu johns]

sir thanks for your answer . Also give an idea how to do this using Matlab .

[Walter Roberson]

This outline;

let total start at 0
start looping
  generate the next term
  if the next term is so small that it cannot affect the total because of limited precision, then exit the loop
  otherwise add the term to the total
  continue at the top of the loop

Except that what you need to be testing is not just whether the current term can change the total because of limited precision: you need to be testing whether the sum of all remaining terms can affect the total.

The way to do that depends on the way the terms get smaller. You need to do some analysis to figure it out, as there are expressions that appear to get smaller and smaller quickly enough that "surely the remainder cannot affect the total", but in fact the infinite tail of remainder is large compared to the terms calculated so far.