Question

simplify the sum
1/(1*2) +2/(1*2*3)+3/(1*2*3*4)+----+n/(1*2*3*---*n*n+1)

Answer 1

\[\frac1{1*2}+\frac{2}{1*2*3}+\frac{1}{1*2*3*4}+...+\frac{n}{1*2*3*...*n*n+1}\]
\[=\sum_{n=1}^{\infty} \frac{n}{(n+1)!}=1\]

Answer 2

the top should be 1,2,3 ... n for numerators.