Consider the following statement:
`P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-1))/(r-1)`
Prove that `P(1)` is true.

Consider the following statement: P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-1))/(r-1) Hence by using the principle of mathematical induction, prove that P(n) is true for all natural numbers n .

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

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+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 If P(k) is true, prove that P(k+1) is true.

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

Consider the statement P(n):1^2+2^2+3^2+…….+n^2-(n(n+1)(2n+1))/6 By assume that P(k) is true, prove that P(k+1) is true.

Consider the following statement : P(n):A^n=[[1+2n,-4n],[n,1-2n]] for all ninN If P(k) is true, then show that P(k+1) is also true.