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

Prove that by using the principle of mathematical induction for all n in N : 41^(n)-14^(n) is multiple of 27

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

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

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

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

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

Prove that by using the principle of mathematical induction for all n in N : (1)/(3.5)+ (1)/(5.7)+ (1)/(7.9)+ ....+(1)/((2n+1)(2n+3))= (n)/(3(2n+3))

Prove that by using the principle of mathematical induction for all n in N : (1)/(2)+ (1)/(4)+ (1)/(8)+ ......+ (1)/(2^(n))= 1-(1)/(2^(n))

Prove that by using the principle of mathematical induction for all n in N : 1.3+3.5+5.7+....+(2n-1)(2n+1)= (n(4n^(2)+6n-1))/(3)

Prove that by using the principle of mathematical induction for all n in N : 1.3+ 2.3^(2)+ 3.3.^(3)+ ....+ n.3^(n)= ((2n-1)3^(n+1)+3)/(4)