Question 70
For each positive integer $n$, let $S_{n}$ be the sum of the infinite geometric series whose first term is $n$ and whose common ratio is $\frac{1}{n+1}$. Determine the least value of $n$ such that
$$
S_{1}+S_{2}+\cdots+S_{n}\gt 5150
$$
$$
S_{1}+S_{2}+\cdots+S_{n}\gt 5150
$$