A statement `p(n)` for a natural number n is given by
`p(n):1/2+1/4+1/8+…….+1/2^n=1-1/2^n`
Verify that `p(1)` is true.

A statement p(n) for a natural number n is given by p(n):1/2+1/4+1/8+…….+1/2^n=1-1/2^n By assuming that p(k) is true for a natural number k, show that p(k+1) is true.

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

Consider the statement '' p(n):9^n-1 is a multiple of 8''. Where n is a natural number. Assuming p(k) is true, show that p(k+1) is true.

Consider the statement P(n):1/1.2+1/2.3+1/3.4+.....+1/{n(n+1)}=n/(n+1) .Show that P(1) is true.

Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 Prove that P(1) is true.

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

Consider the statement P(n):1.2+2.3+3.4+…….+n(n+1)=(n(n+1)(n+2))/3 Prove that P(1) is true.

Consider the statement P(n):1+3+3^2+...+3^(n-1)=(3^n-1)/2 .Show that P(1) is 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.