Create a vector to prove a sum of series?

How can I prove the following series:

π^2/6 = 1 + 1/4 + 1/9 + 1/16 + ...

by creating a vector using colon operators and the function sum.

Thank you so much!

Answer 1

[James Tursa]

Sounds like homework, but I will give you some hints:

v = 1:n; % <-- make a vector with the numbers 1, 2, 3, ..., n

1 ./ whatever % <-- does the divide element-by-element

whatever .^ 2 % <-- does the squaring element-by-element

So you should be able to combine the above operations appropriately to get the approximation you are after. (Although, as a nit, this will not "prove" it).