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 $n$.
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
+1911 
