Consider the statement `P(n):1+3+3^2+...+3^(n-1)=(3^n-1)/2` .Prove by principle of mathematical induction,that P(n) is true for all `n inN`

(b)Prove by the principle of mathematical induction that 3^n>2^n.

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

Using principle of mathematical induction prove that n(n+1)(n+5) is a multiple of 3 for all n in N .

Consider the statement P(n):7^n-3^n is divisible by 4. Verify, by the method of mathematical induction, that P(n) is true for all natural numbers.

Consider the statement '' P(n):x^n-y^n is divisible by x-y ''. Using the principal of Mathematical induction verify that P(n) is true for all natural numbers.

Prove by using the principal of Mathematical Induction P(n)=1+3+3^2+…..+3^(n-1)=(3^n-1)/2 is true for all n in N

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 .

Using mathematical induction prove that (2n+7) lt (n+3)^2 for all n in N

Consider the statement p(n):1^3+2^3+3^3+………..+n^3=[(n(n+1))/2]^-2 Prove the statement using mathematical induction.

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