find the infinite sum - to 3 decimal points.- pic

Question

anonymous · Answer

attachment

anonymous · Answer

eek I can hardly read that...  Was it this?
$$\large \sum_{n=1}^{\infty} \frac{(-1)^n}{(4n+1)^3}$$

If so, first thing first:  try the alternating series test to see if it converges or diverges

anonymous · Answer

thats it, sorry my program saved it so tiny. alterating series test...dammit forgot how to do that

anonymous · Answer

is there any guiding for calculating?

anonymous · Answer

It must has a functional Fourier series.

anonymous · Answer

An alternating series converges if: 
a$_1$ $\ge$ a$_2$ $\ge$ a$_3$ $\ge$...
AND
$$\lim_{k \rightarrow \infty} a_k = 0$$

anonymous · Answer

It does converge here, but as far as to what... and how you get there um... It's going to be ugly and I'm not sure what to tell you other than it has this mess in it: http://mathworld.wolfram.com/HurwitzZetaFunction.html

anonymous · Answer

I still can't get anybody to help me get to the answer on my Calculus question, 2 hours later  :-/

anonymous · Answer

whats your question :)

anonymous · Answer

http://openstudy.com/updates/4ff1d3e7e4b03c0c488a8864