∑(n=1--->∞)(n+1)x^n= ∑(n=1--->∞)[x^(n+1)]'= [∑(n=1--->∞)x^(n+1)]'= [∑(n=0--->∞)x^n-x-1]'=[1/(1-x)-x-1]'=1/[(1-x)^2]-1