Question

Resolva a equuação: Cn,2 + Cn+1, n-1 = 25

Answer 1

Cn,2=n!/2!(n-2)!

Cn+1,n-1= (n+1)!/(n-1)!(n+1-n+1)!=(n+1)!/(n-1)!(2)!

n!/2!(n-2)! + (n+1)!/(n-1)!(2)! = 25
n.(n-1)/2 + (n+1).(n)/2 =25
multiplicando todos por 2:

n.(n-1) + (n+1).(n) = 50
n²-n + n²+n =50
2n²=50
n²=25
n=5