n(n+1)(n+5) is a multiple 3.

Using mathematical induction , show that n(n+1)(n+5) is a multiple of 3 .

If (sqrt(3)-i)^(n)=2^(n) , n in Z, then n is a multiple of

41^(n)-14^(n) is multiple of 27.

Prove that by using the principle of mathematical induction for all n in N : 41^(n)-14^(n) is multiple of 27

Which of the following is a subgroup of the group G = {2^(n)| n in N } under multiplication ?

1.2+2.3+3.4+…………..+n(n+1)=n/3(n+1)(n+2) forall n in N.

If S_(1), S_(2) and S_(3) denote the sum of first n_(1) , n_(2) and n_(3) terms respectively of an A.P.L , then : (S_(1))/(n_(1)) . ( n _(2) - n_(3)) + ( S_(2))/( n_(2)). ( n _(3) - n_(1)) + ( S_(3))/( n_(3)) . ( n_(1) - n_(2)) is equal to :

lim_(n rarr oo) (1+2+3+…...+n)/(n^(2)), n in N is equal to :

If n in N then 3 . 5^(2 n+1)+2^(3 n+1) is divisible by

1/1.2+1/2.3+1/3.4+…………….+1/(n(n+1))=n/(n+1) forall n in N.