Summation of Infinity Terms

I have this question to solve :

Then I have written the code below but it does not work. The main problem is three on index numbers. How to use in MATLAB ? Also I would like to calculate the value of it, not symbolic.

[David Goodmanson]

Hi Berkcan,

since sin(m*pi) = 0 for all integer m, every term in this series is zero. Something has to be wrong here.

[Roger Stafford]

@David. I agree. I didn't notice that.

Answer 1

[Roger Stafford]

In the summation symbol ‘m’ is supposed to range over only the odd positive integers. You have it ranging over all positive integers. Try this:

D = 400/pi*symsum(1/(2*p-1)*sinh((2*p-1)*pi/4)/sinh((2*p-1)*pi)*sin((2*p-1)*pi),p,1,inf);

[David Goodmanson]

Hi Roger, see comment above.

[Berkcan Oz]

Thanks for the code, but I did not understand what you did there. How can I calculate the value of whole sum ?

[Roger Stafford]

@Berkcan: What I did was to replace each p in your expression by 2*p-1. That way as p advances through all possible positive integers, 1, 2, 3, ..., then 2*p-1 will advance through the odd-valued positive integers, 1,, 3, 5, ...

However, you will first have to address the problem pointed out by David, namely that sin(p*pi) is identically zero for all integer-valued p. As it stands, the value of V would be zero.

[Berkcan Oz]

Yeah, I understood right now, so, appreciate to you. How can I fix that problem ? If you tell me a solution, I'll try to write a code then share here.

[Roger Stafford]

You can only fix the problem pointed out by David by correcting the function you wrote originally. Make sure you have it right.