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 August 29th, 2017, 10:34 PM #1 Senior Member   Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 Show that the sum is equal to the value I'm not quite sure where to go with this one. The problem hints at using the binomial expansion, but I'm struggling to see how it will help me here. I tried writing out a couple of terms to no avail as well as expanded the combinatoric portion. I would greatly appreciate any strategies you may have to offer. August 29th, 2017, 11:05 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,127 Thanks: 2336 Write the binomial expansion of $(1 + x)^n$, then list the differences between that polynomial and the left-hand side of the equation you are given to prove. August 29th, 2017, 11:48 PM   #3
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Quote:
 Originally Posted by John Travolski  I'm not quite sure where to go with this one. The problem hints at using the binomial expansion, but I'm struggling to see how it will help me here. I tried writing out a couple of terms to no avail as well as expanded the combinatoric portion. I would greatly appreciate any strategies you may have to offer.
$(1+x)^n = \displaystyle \sum \limits_{k=0}^{n} \dbinom{n}{k} x^k$

differentiate w/respect to $x$

$n(1+x)^{n-1} = \displaystyle \sum \limits_{k=1}^{n}k \dbinom{n}{k} x^{k-1}$

let $x=1$

$n2^{n-1} = \displaystyle \sum \limits_{k=1}^{n} k \dbinom{n}{k}$ Tags equal, show, sum Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post rnck Number Theory 9 May 24th, 2015 04:50 AM evinda Number Theory 0 October 16th, 2014 12:16 PM heinzelmannchen Calculus 3 February 25th, 2014 05:32 AM mathman1990 Abstract Algebra 1 October 5th, 2011 06:10 PM notnaeem Real Analysis 4 August 16th, 2010 01:32 PM

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