Question

If ${ }^{2 n+1} P _{n-1}:{ }^{2 n-1} P _n=11: 21$, then $n^2+n+15$ is equal to :

Answer 1

(n+2)!(2n−1)!(2n+1)!(n−1)!​=2111​
⇒(n+2)(n+1)n(2n+1)(2n)​=2111​
⇒(n+1)(n+2)2n+1​=4211​
⇒n=5
⇒n2+n+15
=25+5+15=45
So , the correct answer is 45.