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

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

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

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)

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

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

Let n(A) = 4 and n(B) = 5 and if in the case of one-one mapping A to B n(A) = 3,n(B) = 4, then the value of n(AxxAxxB) = 6K. Find K.

Find the sum to n terms : (1)/(2) + (3)/(2^(2)) + (5)/(2^(3)) +…+ (2n-1)/(2^(n))

Find the sum to n terms of each of the following series : (1) + (2+3) + (4+5+6)+…

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){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24) , then n is equal to (a) 3 (b) 4 (c) 5 (d) 6