The entries in a certain row of Pascal's triangle are 1,n,…,n,1. The average of the entries in this row is 2. Find n.
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.
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
+1932 
