How can I solve for the sum of infinite terms of the series,4+4.41/2+4.41/2.41/4+...?

Answer 1

I can help you but I cannot give you the answer.

First of all, let's be clear about the sequence: it looks like

4[1 + 83/2 + (83/2)(165/4) + (83/2)(165/4)(329/8) +...

It appears that the recurrence relationship (ignoring the multiple of 4) is:

a_n+1 = a_n(41n+1)/2^[n(n=1)/2]

That means the sequence a_n converges to 0. It is therefore possible that the series converges.

However, this is where my help ends; I do not know how to find the sum.