## anonymous 4 years ago Just something to work on, Prove $$\large \sum \limits_{k=1}^{n} k\times k! = (n+1)! -1$$ without using induction.

1. Zarkon

easy :)...use the same 'trick' I did for the last problem

2. anonymous

Only few things could be somewhat hard for you Zarkon :D but still not all of us know how to read your mind :)

3. Zarkon

k=(k+1)-1

4. anonymous

Yes, telescopic summation :)

5. Mr.Math

I've been trying a different approach, but it doesn't seem to be working :-(

6. myininaya

ffm, zarkon has an alien brain

7. Zarkon

that is ture

8. Zarkon

I feel sorry for all you HUmons

9. anonymous

Yes, all these professors seems to have that :P

10. asnaseer

\begin{align} \sum \limits_{k=1}^{n} k\times k!&=\sum \limits_{k=1}^{n} ((k+1)-1)\times k!\\ &=\sum \limits_{k=1}^{n} (k+1)! - k!\\ &=2!-1!+3!-2!+4!-3!+...+(n+1)!-n!\\ &=(n+1)!-1 \end{align}using hint given by Zarkon and telescopic sum as ffm indicated

11. myininaya

I like that :)

12. asnaseer

all credit and trademarks belong to Zarkon and ffm :D

13. myininaya

how much do they get paid, ffm?

14. asnaseer

Zarkon especially - he seems to have a brain like a laser! :D

15. Zarkon

Its Planet doom university...they really cultivate the young alien mind.

16. Mr.Math

Sometimes the thought that he has got supernatural powers occurs to me :-P

17. asnaseer

:D lol! Zarkon

18. anonymous

Myin, more than they could possibly spend, (they spend most of the time doing maths)

19. anonymous

one time someone asked me why they call it "telescope" which was the first time i realized that it was not obvious. i guess modern telescopes don't actually "telescope"

20. myininaya

Zarkon can you use that money to see me to plant doom university.

21. Mr.Math

22. myininaya

send* lol

23. anonymous

@send?

24. Zarkon

only if you lived there...the out of planet tuition is outragious.

25. asnaseer

I'd be happy to stow away in the luggage compartment!

26. myininaya

do you fold well?

27. Mr.Math

haha

28. asnaseer

@satellite - we still have telescopic aerials, poles, etc - you could use those as examples? :) @myininaya - yes - I was trained especially for that by being fed lots of soft bananas :D

29. Mr.Math

Looks like asnaseer has been to other planets too, haven't you?

30. asnaseer

Shhhh.... Mr.Math - you are ruining my plan to rule the Universe.... ;-)

31. myininaya

Well anyways great question and great answer to all of the aliens involved.

32. anonymous

Myin: Take a look at this M.SE thread ( http://math.stackexchange.com/questions/18576/)

33. Mr.Math

Whops! sorry.

34. myininaya

so this is where you got the problem ffm? from this universe?

35. anonymous

lol no, I just got it from MR.M's previous question.