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

- anonymous

- chestercat

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- Zarkon

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

- anonymous

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

- Zarkon

k=(k+1)-1

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## More answers

- anonymous

Yes, telescopic summation :)

- Mr.Math

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

- myininaya

ffm, zarkon has an alien brain

- Zarkon

that is ture

- Zarkon

I feel sorry for all you HUmons

- anonymous

Yes, all these professors seems to have that :P

- 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

- myininaya

I like that
:)

- asnaseer

all credit and trademarks belong to Zarkon and ffm :D

- myininaya

how much do they get paid, ffm?

- asnaseer

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

- Zarkon

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

- Mr.Math

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

- asnaseer

:D lol! Zarkon

- anonymous

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

- 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"

- myininaya

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

- Mr.Math

Me too please!

- myininaya

send* lol

- anonymous

- Zarkon

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

- asnaseer

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

- myininaya

do you fold well?

- Mr.Math

haha

- 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

- Mr.Math

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

- asnaseer

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

- myininaya

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

- anonymous

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

- Mr.Math

Whops! sorry.

- myininaya

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

- anonymous

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

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