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-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: 2+5+8+11++(3n-1)=(1)/(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+3^(2)++3^(n-1)=(3^(n)-1)/(2)

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)

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 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+2+2^(7)=2^(n+1)-1 for all n in N