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/(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+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 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+2. 3+3. 4++n(n+1)=(n(n+1)(n+2))/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)/(1.4)+(1)/(4.7)+(1)/(7.10)++(1)/((3n-1)(3n+2))=(n)/(3n+1)

Prove the following by the principle of mathematical induction: 1.2+2.3+3.4++n(n+1)=(n(n+1)(n+2))/(3)

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 the principle of mathematical induction: 1+2+2^(7)=2^(n+1)-1 for all n in N