Prove by the principle of mathematical induction that for all `n belongs to N :\ ` `1/(1. 3)+1/(3.5)+1/(5.7)++1/((2n-1)(2n+1))=n/(2n+1)`

Prove by the principle of mathematical induction that for all n in N : 1+4+7++(3n-2)=1/2n(3n-1)

Prove by the principle of mathematical induction that for all n in N : 1^2+2^2+3^2++n^2=1/6n(n+1)(2n+1)

Prove the following 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 by the principal of mathematcal induction that for all n in N . 1^(2) + 3^(2) + 5^(2) + …… + (2n - 1)^(2) = (n(2n - 1) (2n + 1))/(3)

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))

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

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

Prove by the principle of mathematical induction 4^(n)+ 15n - 1 is divisible 9 for all n in N .

Prove the following by using the principle of mathematical induction for all n in N : (1+3/1)(1+5/4)(1+7/9)...(1+((2n+1))/(n^2))=(n+1)^2

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