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)/(2.5)+(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)/(3.7)+(1)/(7.11)+(1)/(11.15)++(1)/((4n-1)(4n+3))=(n)/(3(4n+3))

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

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

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+1)>2n+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+2.4+3.5++(2n-1)(2n+1)=(n(4n^(2)+6n-1))/(3)