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

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 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 Nvdots1+2+3+...+n<(1)/(8)(2n+1)^(2)

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 Nvdots1+3+3^(2)+...+3^(n-1)=((3^(n)-1))/(2)

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 Nvdots1.2+2.2^(2)+3.2^(2)+...+n.2^(n)=(n-1)2^(n+1)+2

Prove the following by using the Principle of mathematical induction AA n in N 2^(3n-1) is divisble by 7.

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