Just something to work on,

Prove $ \large \sum \limits_{k=1}^{n} k\times k! = (n+1)! -1 $ without using induction.

Question

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

zarkon · Answer

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

anonymous · Answer

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

zarkon · Answer

k=(k+1)-1

anonymous · Answer

Yes, telescopic summation :)

mr.math · Answer

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

myininaya · Answer

ffm, zarkon has an alien brain

zarkon · Answer

that is ture

zarkon · Answer

I feel sorry for all you HUmons

anonymous · Answer

Yes, all these professors seems to have that :P

asnaseer · Answer

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

myininaya · Answer

I like that
:)

asnaseer · Answer

all credit and trademarks belong to Zarkon and ffm :D

myininaya · Answer

how much do they get paid, ffm?

asnaseer · Answer

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

zarkon · Answer

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

mr.math · Answer

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

asnaseer · Answer

:D lol! Zarkon

anonymous · Answer

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

anonymous · Answer

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 · Answer

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

mr.math · Answer

Me too please!

myininaya · Answer

send* lol

anonymous · Answer

@send?

zarkon · Answer

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

asnaseer · Answer

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

myininaya · Answer

do you fold well?

mr.math · Answer

haha

asnaseer · Answer

@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 · Answer

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

asnaseer · Answer

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

myininaya · Answer

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

anonymous · Answer

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

mr.math · Answer

Whops! sorry.

myininaya · Answer

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

anonymous · Answer

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