Thread: Help with calculating a summation

Hi there,

I have a trigonometrical-series type of solution as follows:



I am having trouble calculating the sum part of the expression. Let's assume

and x = 0 and divide through by , then I get the sum part to be:



The reference I am using gives the overall answer to be:



but I am getting much smaller answers. Could anyone suggest what I might be doing wrong?

Any help would be much appreciated

Your sum has no limits, so I'm assuming an infinite series starting at n = 0. Notice this is an alternating series with the magnitude of the terms decreasing to 0 as n goes to infinity. So the series converges and you know the value of a partial sum with m term differs from the value of the series by at most the magnitude of the (m+1)st term. With your calculator you find that the magnitude of the 3nd term is of the order of E-28. So just the sum of the 1st two terms is very close to the true value. I find the answer you gave to be correct.

Thanks johng!

I just reached the same conclusion - you beat me to it! I had initally started at n = 1 and seeing as the n = 0 part contributes the most, my answer was much too small.

I have run into another similar problem, perhaps you could help me with that too? The sum is:



we can let be a constant. The limits in this case are n = 1 to infinity (I haven't mastered that in latex yet sorry...)

Essentially, I am getting answers that tend to oscillate for different values of r (ranging from 0 to 1).

I have tried to break down each part of the sum to see how it contributes, but I am not having much luck.

Again, any light thrown on this would be very much appreciated!