" (ii) "3^(4n+1)+2^(2n+2)quad [n geqslant0]" is a multiple of "7" ."

If ninNN , then by principle of mathematical induction prove that, 3^(4n+1)+2^(2n+2)" "[nge0] is a multiple of 7.

Prove that 1 + w ^( n ) + w ^( 2n) = 3, if n is multiple of 3 1 + w ^( n ) + w ^( 2n) = 0, if n is not multiple of 3 n in N

The sum to 100 terms of the series 1.2.3. + 2.3.4. + 3.4.5. + …+ n(n + 1) (n+2) + …. is integral multiple of

The sum to 100 terms of the series 1.2.3. + 2.3.4. + 3.4.5. + …+ n(n + 1) (n+2) + …. is integral multiple of

Let P (n) be the statement 2^(3n) - 1 is integral multiple of 7. Then P (3) is true.

By induction prove that, 7^(2n)+2^(3(n-1))*3^(n-1) is a multiple of 25 for all ninNN .

If 1;w;w^(2) are cube root of unity and n is a positive integer; then 1+w^(n)+w^(2n)={3; When n is multiple of 3;0; when n is not a multiple of 3

If 1;w;w^2 are cube root of unity and n is a positive integer;then 1+w^n+w^(2n) = {3; When n is multiple of 3; 0; when n is not a multiple of 3