Consider the statement `P(n):2^(3n) -1` is divisible by 7
If p(k) is true, show that p(k+1) is also true

Consider the statement P(n):7^n-3^n is divisible by 4. Show that P(1) is true.

Given P(n):3^(2n) -1 is divisible by 8. If P(k) is true then prove P(k+1) is true.

Consider the statement P(n):2^(3n) -1 is divisible by 7 Is the statement p(1) true? justify your answer

Let P(n) denotes the statement 10^(2n-1)+1 is divisible by 11. If P(m) is true, prove that P(m+1) is also true.

Consider the statement '' P(n):x^n-y^n is divisible by x-y ''. Show that P(1) is true.

Consider the statement P(n)=1+3+3^2+….+3^(n-1)=(3^n-1)/2 (b)If P(k) is true,prove that P(k+1) is also true.

Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 If P(k) is true, prove that P(k+1) is also true

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assume that P(k) is true for a natural number k, Verify that P(k+1) is true.

For all nge1 , prove that p(n):2^(3n)-1 is divisible by 7.

Given P(n):3^(2n) -1 is divisible by 8 Check whether P(1) is true.