how can i calcutate Σ n*(1/3)^(n-1)/(1+(1/3)^n), where n goes from 1 to +inf?
By the ratio test, the series converges.
sum_(n=1)^∞ (n (1/3)^(n - 1))/(1 + (1/3)^n)≈1.9193300521..........etc.
our professor made us calculate this sum. shouldnt i submit as my final answer 2, sincie it would be a bit crazy, if he wanted us to sumbit 1,9193300, without the use of a calculator?
