If `P(n)` be the statement ` 2^ngtn^n and if P(m)` is true, show tht `P(m+1)` is also true

If P(n) is the statement 2^ngeq3n , and if P(r) is true, prove that P(r+1) is true.

Let P(n) be the statement: 2^n >= 3n . If P(r) is true, show that P (r + 1) is true. Do you conclude that P(n) is true for all n in N

Let P(n) be the statement ''(3)^(n)gt n'' . If P(n) is true , prove that P(n + 1) is true.

If P(n) is the statement n^2+n is even, and if P(r) is true then P(r+1) is true.

Let P(n) be the statement "3^n > n" . If P(n) is true, P(n+1) is also true.

If P (n) is the statement n^2> 100" , prove that whenever P(r) is true, P(r+1) is also true.

If P(n) be the statement " 10n+3 is a prime number", then prove that P(1) and P(2) are true but P(3) is false.

If P(n) is the statement n(n+1)(n+2) is divisible is 12 prove that the statements P(3) and P(4) are true, but that P(5) is not true.

If P(n) is the statement n^3+n is divisible by 3, prove that P(3) is true but P(4) is not true.

If P(n) is the statement "2^(3n)-1 . Is an integral multiple 7", and if P(r) is true, prove that P(r+1) is true.