Find the value of n if: `2n!`n!`=(n+1)(n-1)(!(2n-1)!`

Find the value of n if: (n+1)! =12.(n-1)!

Find the value of n if: (i) (n+2)! = 12n! (ii) (n+2)! = 60(n-1)! (iii) (n+3)! = 2550 (n+1)! (iv) (n-2)! = 132. (n-4)! .

Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

Find the value of 1/(81^n)-(10)/(81^n)^(2n)C_1+(10^2)/(81^n)^(2n)C_2-(10^3)/(81^n)^(2n)C_3++(10^(2n))/(81^n) .

Find the value of (Sigma_(r=1)^(n) 1/r)/(Sigma_(r=1)^(n) k/((2n-2k+1)(2n-k+1))) .

The value of lim_(n->oo)[(2n)/(2n^2-1)cos(n+1)/(2n-1)-n/(1-2n)dot(n(-1)^n)/(n^2+1)]i s 1 (b) -1 (c) 0 (d) none of these

If n in NN , then find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) .