Prove the following by using the principle of mathematical induction for all `n in N`:`1/(2. 5)+1/(5. 8)+1/(8. 11)+dotdotdot+1/((3n-1)(3n+2))=n/((6n+4))`

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+...+(1)/((3n-1)(3n+2))=(n)/((6n+4))=(n)/((6n+4))

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+1)>2n+1

Prove the following by using the principle of mathematical induction for all n in Nvdots(2n+7)<(n+3)^(2)

Prove the following by using the principle of mathematical induction for all n in Nvdots1+2+3+...+n<(1)/(8)(2n+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 for all n in Nvdots(1)/(1.4)+(1)/(4.7)+(1)/(7.10)+...+(1)/((3n-1)(3n+1))=(n)/((3n+1))

Prove the following by using the principle of mathematical induction for all n in Nvdots10^(2n-1)+1 is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in Nvdotsn(n+1)(n+5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2)+(1)/(4)+(1)/(8)+...+(1)/(2^(n))=1-(1)/(2^(n))

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(3.5)+(1)/(5.7)+(1)/(7.9)+...+(1)/((2n+1)(2n+3))=(n)/(3(2n+3))