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/(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/(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-1)(3n+2))=(n)/(3n+1)

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+3+3^2++3^(n-1)=(3^n-1)/2

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

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