
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 29th, 2017, 09:34 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, 10:05 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,826 Thanks: 2160 
Write the binomial expansion of $(1 + x)^n$, then list the differences between that polynomial and the lefthand side of the equation you are given to prove.

August 29th, 2017, 10:48 PM  #3  
Senior Member Joined: Sep 2015 From: USA Posts: 2,500 Thanks: 1372  Quote:
differentiate w/respect to $x$ $n(1+x)^{n1} = \displaystyle \sum \limits_{k=1}^{n}k \dbinom{n}{k} x^{k1}$ let $x=1$ $n2^{n1} = \displaystyle \sum \limits_{k=1}^{n} k \dbinom{n}{k}$  

Tags 
equal, show, sum 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Need Help : to show 2 almost equal fraction is not equal using contradiction??  rnck  Number Theory  9  May 24th, 2015 03:50 AM 
Show that the sets are equal  evinda  Number Theory  0  October 16th, 2014 11:16 AM 
Show that the second derivative is equal to 4y  heinzelmannchen  Calculus  3  February 25th, 2014 04:32 AM 
Show that MF(0) does not equal FM(0)  mathman1990  Abstract Algebra  1  October 5th, 2011 05:10 PM 
want to show that show that two infinite summations R equal  notnaeem  Real Analysis  4  August 16th, 2010 12:32 PM 