Question 11
For each positive integer $k$, let $f(k)=\frac1{(k+2)\times(k!)}$. Find the largest positive integer $n$ such that
$$f(1)+f(2)+\cdots+f(n)<\frac12-\frac1{2019!}.$$
($k!$ is the product of the first $k$ positive integers.)
$$f(1)+f(2)+\cdots+f(n)<\frac12-\frac1{2019!}.$$
($k!$ is the product of the first $k$ positive integers.)