Find n, if `n/(6!) = 1/(5!) + 1/(4!)`

Find n, if n/(5!) = 3/(6!) + 1/(4!)

Find n if ""^(n-1)P_(3) : ""^(n)P_(4)=1:9 .

Find n ,if(n+1)! =12xx(n-1)!dot

Prove that by using the principle of mathematical induction for all n in N : (1)/(2.5)+ (1)/(5.8) + (1)/(8.11)+ ...+(1)/((3n-1)(3n+2))= (n)/(6n+4)

Evaluate : underset(nrarrinfty)lim [1/n + 1/(n+1)+ 1/(n+2) + .... +1/(4n)]

Find the sum of 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+ ...,

For the sequence {u_(n)} if u_(1) = (1)/(4) and u_(n+1) = (u_(n))/(2+u_(n)) , find the value of (1)/(u_(50)) .

Prove that by using the principle of mathematical induction for all n in N : (1)/(1.2.3)+ (1)/(2.3.4)+ (1)/(3.4.5)+....+ (1)/(n(n+1)(n+2))= (n(n+3))/(4(n+1)(n+2))

If sum_(r=0)^(n)((r+2)/(r+1)).^n C_r=(2^8-1)/6 , then n is (A) 8 (B) 4 (C) 6 (D) 5

Evaluate (with the help of definite integral) underset(nrarr infty) It ((1)/(n+1) + (1)/(n+2) + ….. + (1)/(6n))