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anonymous
 one year ago
Evaluate :
3!/2  4!/3 + 5!/4  6!/5 + .... + 2013!/2014  2014!/2013
anonymous
 one year ago
Evaluate : 3!/2  4!/3 + 5!/4  6!/5 + .... + 2013!/2014  2014!/2013

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Empty
 one year ago
Best ResponseYou've already chosen the best response.0Shouldn't the second to last term really be 2013!/2012 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oopsss..sorry i was typo there. Yeah the second last should be 2013!/2012

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Fun problem I'll say that! I don't know where to begin hmm...

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Another approaching \(a_1= \dfrac{3!}{2}\\a_3=\dfrac{5!}{4}\\a_5=\dfrac{7!}{6}\\\) while \(a_2= \dfrac{4!}{3}\\a_4=\dfrac{6!}{5}\\a_6=\dfrac{8!}{7}\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1So our sequence is \(a_n= (1)^{n+1}\dfrac{(n+2)!}{n+1}\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1I give up!! hehehe.. it's above my head!!

Empty
 one year ago
Best ResponseYou've already chosen the best response.0What you deleted everything AND gave up?!

Empty
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 http://www.brainyquote.com/quotes/quotes/a/alberteins109012.html

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hey! what do you need help with?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0need a way and solution :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Isn't that \[(1)^{n+1} (n!+(n+1)!)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Telescopes quite nicely

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what's next @mukushla ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3do you see see how \(\dfrac{(n+2)!}{n+1} \) simplifies to \(n! + (n+1)!\) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(n+1)!/n = (n+1)n(n1)!/n = (n+1)(n1)! hmmm...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[\begin{align}\dfrac{(n+2)!}{n+1} &= \dfrac{(n+2)(n+1)n!}{n+1} \\~\\ &= (n+2)n! = (\color{blue}{n+1}+1)n!\\~\\ & = (n+1)n! + n! \\~\\ &= (n+1)!+n!\end{align}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ah yes i see now :) sorry i look n+1 but should be n+2. Whats next ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3familiar with sigma notation ? \(\sum\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3the given sum is same as : \[ [(1+1)!+1!]  [(2+1)!+2!] + [(3+1)!+3!] \cdots [(2012+1)!+2012!] \]

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1Wooooooooooooooah!! it is nice.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3or \[ [2!+1!]  [3!+2!] + [4!+3!] \cdots [2013!+2012!] \]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3please medal loser/mukushla, not meh

Loser66
 one year ago
Best ResponseYou've already chosen the best response.1You work, why medal me?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Looks the series is nice but not sure which numbers can be cancels ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3i didnt use my brain, i just used ur work for general term and mukushla's idea of telescoping

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01!  2012! as finally ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[ [2!+1!]  [3!+2!] + [4!+3!] \cdots [2013!+2012!] \] Let me break it like below : \[ \begin{align} &[2!+1!]\\~\\ &  [3!+2!] \\~\\ &+ [4!+3!] \\~\\ &\cdots \\~\\ &[2013!+2012!] \end{align}\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.31!  2012! is wrong, try again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ah looks diagonal numbers can be cancels. The rest is 1!  2013! Hehe, thanks @ganeshie8 for ur leader
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