## anonymous 5 years ago help me please... does the series converges? if it does , try to find the sum. summation n=1 to infinity n/(2^n) how should i start solving this question ????

1. anonymous

The ratio test shows that this is convergent:$\frac{a_{n+1}}{a_{n}}=\frac{\frac{n+1}{2^n}}{\frac{n}{2^n}}=\frac{n+1}{2n}=\frac{1+\frac{1}{n}}{2}$Taking the limit as n approaches infinity shows that the ratio is 1/2, which is less than 1 (which is what is needed if the ratio test is to work).

2. anonymous

thank you