Prove the following by using the principle of mathematical induction for all `n in N`:`10^(2n-1)+1`is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in N : 3^(2n+2)-8n-9 is divisible by 8.

Prove the following by using the principle of mathematical induction for all n in N : x^(2n)-y^(2n) is divisible by x + y .

Prove the following by using the principle of mathematical induction for all n in N : (2n+7)<(n+3)^2 .

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 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 by using the principle of mathematical induction that for all n in N, 10^(n)+(3xx4^(n+2))+5 is divisible by 9 .

Prove the following by using the principle of mathematical induction for all n in N : 1 + 2 + 3 + ... + n <1/8(2n+1)^2 .

Prove the following by the principle of mathematical induction: \ (a b)^n=a^n b^n for all n in Ndot

Prove the following by using the principle of mathematical induction for all n in N : 1/(2. 5)+1/(5. 8)+1/(8. 11)+...+1/((3n-1)(3n+2))=n/((6n+4))