Question

Find the sum \(\large \sum_{k=1}^{n} k!(k^2+k+1).\)

Answer 1

\( \large \sum \limits_{k=1}^{n} k!(k^2+k+1) = (n+1)!(n+1)-1 \)

PS: Latex Tip included ;-)

Answer 2

You should show work, so others can learn :-)

Answer 3

\[k^2+k+1=(k+1)^2-k\]

Answer 4

is my hint good enough?

Answer 5

Yes.

Answer 6

One more hint, \( \large \sum \limits_{k=1}^{n} k\times k! = (n+1)! -1\)

Answer 7

oops MR.Math is great :)

Answer 8

lol, I already know the answer. I just wanted to post something, and I think it's a nice problem.

Answer 9

haha :)

Answer 10

Mr.Math here: http://openstudy.com/study#/updates/4f2ebf12e4b0571e9cbaf294 ;-)