If 1+3+5+…..+(2n+1)=1296, find n.

If (n+1)! = 12 [(n-1)!], find n.

If (n+2)! = 60 [(n-1)!], find n.

Using principle of mathematical induction, prove that: 1+3+5+………..+(2n-1)= n^2 .

Given L, = {1,2, 3,4},M= {3,4, 5, 6} and N= {1,3,5} Find L-(M⋃N).

If "^(2n)C_3 : ^nC_2= 12: 1 , find n .

Prove the following by using the principle of mathematical induction for all n in N :- 1.3 + 3.5 + 5.7 +...+ (2n-1)(2n+1)=(n(4n^2 +6n-1))/3

Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n*1 also, find the coefficient of x^(n-1) in th cxpansion of (1+2x+3x^(2)+"...."nx^(n-1))^(2) .

Prove that : (2n) ! = 2^n (n!)[1.3.5.... (2n-1)] for all natural numbers n.

Prove the following by using the principle of mathematical induction for all n in N :- 1^2+3^2+5^2 + ...+(2n-1)^2=(n(2n-1)(2n+1))/3 .

For the proposition P(n), given by , 1+3+5+.........+(2n-1) = n^2 +2 , prove that P(k) is true implies P(k + 1) is true. But, P(n) is not true for all n in N.