Determine the interval of convergence of the series

Question

anonymous · Answer

$$\sum_{n=1}^{\infty} (x-(3/4))^n/(n2^n)$$

anonymous · Answer

Some clues here.... http://www.wolframalpha.com/input/?i=sum+1+to+10+%28x-%283%2F4%29^n%29%2Fn2^n

anonymous · Answer

my knowledge of series is a bit.... rusty... so here goes. I used the ratio test which states that the if the limit as n -> infinity of the ratio of the n+1 term divided by n is less than 1, the series is convergent. So if the limit of ((x-3/4)^(n+1)/(n+1)(2^(n+1))*(n2^2)/(x+3/4)^n is less than 1 it's convergent. I simplified and got (x-3/4)*n/2(n+1) (hope this is right)... this results in (x-3/4)/2 so the interval is where (x-3/4)/2 is less than 1 or x<11/4.

anonymous · Answer

oops in that second sentence... i meant n+1 term divided by nth term