MATLAB: Create a vector to prove a sum of series

colon operatorshomeworksumvector

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!

Best Answer

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).

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MATLAB: Summation of an infinate series

That can be done in 3 lines of code tops. However, giving you the solution for your assignment straight away does not seem fair.

Finding the nmax satisfying your threshold should not be hard analytically.

After that, you can use the builtin function sum to calculate the sum of the elements of a vector containing the terms 1/n^2 up to the threshold you calculated.

Take a look at the elementwise operations ./ and .^2.

Total, three lines of code, if you build the vector in a separate instruction

 1) calculate the threshold
 2) build the vector
 3) sum the vector

MATLAB: Vectors and Sum operation

R = 1/sum(1./y);

y is a vector. You want to divide EACH of the elements of y into 1. So you use the ./ operator, which is designed to solve element-wise operations. (Just like the .* and .^ operators.)

The other divide is a scalar/scalar operation, so / works fine there, although ./ would also be acceptable. That is:

R = 1./sum(1./y);

would also work.

Finally, there was no need to put a parens around y in your original line. So while it is fine to add additional parens if you are not sure you need them in some spot, too many parens that need not be there will only make things confusing, hard to read and debug.

Best Answer

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MATLAB: Summation of an infinate series

MATLAB: Vectors and Sum operation

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