Question

∑(k=1)→n k/(k+1)! .. some help please with this sum..

Answer 1

\[\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{n}{(n+1)!}\]
hmmm

Answer 2

1/2

5/6

23/24

23/24 + 4/120 .... might need the wolf

Answer 3

http://www3.wolframalpha.com/input/?i=sum+0+to+n+%28k%2F%28k%2B1%29%21%29

Answer 4

1/2 5/6 23/24 23/24 + 4/120 .... might need the wol

Answer 5

you could have done this without the wolf if you spotted the pattern in the partial sums listed by @amistre64:\[\begin{align}
k=1 &\qquad \frac{1}{2} &= \frac{2!-1}{2}!\qquad &= 1-\frac{1}{2!}\\
k=2 &\qquad \frac{5}{6} &= \frac{3!-1}{3!}\qquad &= 1-\frac{1}{3!}\\
k=3 &\qquad \frac{23}{24} &= \frac{4!-1}{4!}\qquad &= 1-\frac{1}{4!}\\
k=4 &\qquad \frac{119}{120} &= \frac{5!-1}{5!}\qquad &= 1-\frac{1}{5!}\\
...\\
k=n &\qquad ... &= \frac{(n+1)!-1}{(n+1)!}\qquad &=1-\frac{1}{(n+1)!}\\
\end{align}\]