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 + 1/4 + 1/8+ ……..+ (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 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+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+3^2+5^2+dotdotdot+(2n-1)^2=(n(2n-1)(2n+1))/3

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 + 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 N 1 + 2 + 2^2 + …..+2^n = 2^(n+1) -1