Prove the following by using the principle of mathematical induction for all `n in N`:`41^n-14^n`is a multiple of 27.

Prove the following by using the principle of mathematical induction for all n in Nvdots41^(n)-14^(n) is a multiple of 27

Prove the following by using the principle of mathematical induction for all n in N 3^n gt 2^n

(a)Prove the following by using the principle of mathematical induction for all n in N:2^n<3^n .

Prove the following by using the principle of mathematical induction for all n in N n(n+1)(n+5) is a multiple of 3

(b)Prove the following by using the principle of mathematical induction for all n in N:n^2+n is even.

Prove the following by using the principle of mathematical induction for all n in N : n(n + 1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N : n(n + 1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N :- n(n +1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in Nvdotsn(n+1)(n+5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N (1+x)^n lt= (1+nx)