If `P(n) :1+4+7…….+(3n-2)=(1)/(2)n(3n-1)`.Verify P(n) for n =1,2.

Let P(n):1+3+5+……+(2n+-1)= n^'2(i)Verify P(1) is true.

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. Verify the statement for n=2.

If ^(n+5)P_(n+1)=(11(n-1))/(2)n+3P_(n), find n

By using the principle of mathematical induction , prove the follwing : (1)/(1.4) + (1)/(4.7) + (1)/(7.10) + ………..+ (1)/((3n - 2)(3n+1)) = (n)/(3n + 1) , n in N

If .^(2n+1)P_(n-1): .^(2n-1)P_(n)=3:5 , find n.

If P(n ,5): P(n ,3)=2:1 find n

Consider the statement P(n):1x2+2x3+3x4+………+n(n+1)='(n(n+1)(n+2)/3' (a)Verify that P(3) is true.

Find n, ""^(n+5)P_(n+1)=(11)/(2)(n-1)*""^(n+3)P_(n).

Find n, ""^(n+5)P_(n+1)=(11)/(2)(n-1)*""^(n+3)P_(n).