Rewrite $\sum_{n=1}^k{(n-1)/n!}$ and write the formula in terms of k

Question

Rewrite $\sum_{n=1}^k{\frac{n-1}{n!}}$

I have turned it into $\frac{1}{n}*\frac{1}{(n-2)!}$ but do not know where to go from here.

Answer 1

Hint: $$ \sum_{n=1}^k{\frac{n-1}{n!}} = \sum_{n=1}^k \frac{1}{(n-1)!} - \sum_{n=1}^k \frac{1}{n!}. $$

Answer 2

$$S=\sum_{n=1}^k(f(n-1)-f(n))$$

$$=f(0)-f(k)$$ where $f(n)=\dfrac1{n!}$