Prove the following by using the principle of mathematical induction for all `n in N`:`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 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 for all n in N 1+2+3+…….+n lt 1/8 (2n+1)^2

Prove the following by using the principle of mathematical induction for all n in N :- 1 +2 + 3 +...+n < 1/8(2n+1)^2 .

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

Prove the following by using the principle of mathematical induction for all n in N 4+8 + 12 + …….+4n = 2n (n+1)

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

Prove the following by using the principle of mathematical induction for all n in N : (1+3/1)(1+5/4)(1+7/9)...(1+((2n+1))/(n^2))=(n+1)^2

(a)Prove the following by using the principle of mathematical induction for all n in N:2^1+2^2+……..+2^n=2^(n+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))