For $n,k\in \mathbb{N}$ let $$T(n,k)=\frac{1}{(n+1)!}+\frac{1}{(n+2)!}+\frac{1}{(n+3)!}+...+\frac{1}{(n+k)!}$$
Which of the below statement(s) hold true
(A)$T(n,k)\geq \frac{1}{2}$
(B)$T(n,k)> \frac{1}{(n-1)!}$
My Attempt
I am trying to create a geometric progression $T(n,k)=\frac{1}{(n+1)!}+\frac{1}{(n+2)!}+\frac{1}{(n+3)!}+...+\frac{1}{(n+k)!}<\frac{1}{n+1}+\frac{1}{(n+1)^2}+...$
but am not getting anywhere