Prove the following by the principle of mathematical induction: `1/(3. 7)+1/(7. 11)+1/(11. 15)+.....+1/((4n-1)(4n+3))=n/(3(4n+3))`

Prove the following by the principle of mathematical induction: 1/(1. 4)+1/(4. 7)+1/(7. 10)+....+1/((3n-2)(3n+1))=n/(3n+1)

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

Prove the following by the principle of mathematical induction: 1/(3. 5)+1/(5. 7)+1/(7. 9)+1/((2n+1)(2n+3))=n/(3(2n+3))

Prove the following by the principle of mathematical induction: 1+3+3^2++3^(n-1)=(3^n-1)/2

Prove the following by the principle of mathematical induction: 1/(1. 2)+1/(2. 3)+1/(3. 4)++1/(n(n+1))=n/(n+1)

Prove the following by the principle of mathematical induction: 1/2+1/4+1/8++1/(2^n)=1-1/(2^n)

Prove the following by the principle of mathematical induction: 2+5+8+11++(3n-1)=1/2n\ (3n+1)

Prove the following by the principle of mathematical induction: \ 1^2+3^2+5^2++(2n-1)^2=1/3n(4n^2-1)

Prove the following by the principle of mathematical induction: 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

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))