## Proof of sum results

I was going through some of my notes when I found both these sums with their results x0+x1+x2+x3+…=11−x,|x|<1 0+1+2x+3×2+4×3+…=1(1−x)2 I tried but I was unable to prove or confirm that these results are actually correct, could anyone please help me confirm whether these work or not? Answer 1−xn+11−x=1+x+x2+⋯+xn, now if n→∞ and |x|<1 we get … Read more