Question

· If P2n+1, n-1) : P2n-1, n) = 3:.5 then find n
MP 2014​

Answer 1

Answer:

Given equation is

2n+1

P

n−1

:

2n−1

P

n

=3:5

So,

(2n−1−n)!

(2n−1)!

(2n+1−n+1)!

(2n+1)!

=

5

3

⇒

(n+2)(n+1)n(n−1)!

(2n+1)(2n)(2n−1)!

×

(2n−1)!

(n−1)!

=

5

3

Solving we get

⇒

(n+1)(n+2)

2(2n+1)

=

5

3

⇒20n+10=3n

2

+9n+6

⇒3n

2

−11n−4=0

⇒3n

2

−12n+n−4=0

⇒3n(n−4)+1(n−4)=0

∴n=4