Simplify the ratio of factorials 9n19n1Solution 9n 1 9n 1 we

Simplify the ratio of factorials (9n-1)!/(9n+1)!

( 9n -1)!/( 9n +1)!

we can write : (9n +1)! = (9n+1)(9n)(9n -1)!

So, ( 9n -1)!/( 9n +1)! = ( 9n -1)!/(9n+1)(9n)(9n -1)!

----> (9n -1)! can be cancelled both in numerator and denominator:

( 9n -1)!/( 9n +1)! = 1/( 9n+1)9n)

= 1/( 81n^2 + 9n)