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A row of Pascal's triangle reads \[1,n,\ldots,n,1\] The arithmetic mean of the entries in this row of Pascal's triangle is $2048$. Find $n$.

 Apr 24, 2015

Best Answer 

 #1
avatar+33603 
+14

This question only makes sense if the first row of Pascal's triangle is taken to be   1  1  (the first row is often given as just the number 1 on its own).  Given this then the sum of numbers in row n is 2n and there are n+1 numbers so the arithmetic mean is 2n/(n+1).  This equals 2048 when n = 15.

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 Apr 25, 2015
 #1
avatar+33603 
+14
Best Answer

This question only makes sense if the first row of Pascal's triangle is taken to be   1  1  (the first row is often given as just the number 1 on its own).  Given this then the sum of numbers in row n is 2n and there are n+1 numbers so the arithmetic mean is 2n/(n+1).  This equals 2048 when n = 15.

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Alan Apr 25, 2015

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