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avatar+1791 

The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is 2. Find $n$.

 Oct 12, 2023
 #1
avatar+624 
-1

The sum of all the entries in the row of Pascal's triangle is 1+n+2n+⋯+2n+1=2n(n+1). Since the average of the entries is 2, we have [\frac{2n(n + 1)}{n + 1} = 2,] which simplifies to n=6​.

 Oct 12, 2023
 #2
avatar+128794 
+1

  Avg of nth row of Pascal's Triangle =  2^n  / ( n + 1)

 

So

 

2^n / (n + 1)   = 2

 

2^n  = 2(n + 1)

 

n = 3

 

                        1                            Avg  = 1

                    1      1                        Avg =  1

                  1     2     1                    Avg  = 4/3

                1   3     3     1                 Avg  =  2

 

n =  3

 

cool cool cool

 Oct 12, 2023

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