" 5."(1)/(2)+(1)/(4)+(1)/(8)+...+(1)/(2^(n))=(1-(1)/(2^(n)))

For all ninNN , prove by principle of mathematical induction that, (1)/(2)+(1)/(4)+(1)/(8)+ . . .+(1)/(2^(n))=1-(1)/(2^(n)) .

Prove the following by the principle of mathematical induction: (1)/(2)+(1)/(4)+(1)/(8)++(1)/(2^(n))=1-(1)/(2^(n))

(1)/(2)+(1)/(4)+(1)/(8)+(1)/(16)+......+(1)/(2^(n))=1-(1)/(2^(n))

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

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

If a_(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+(1)/(5)+ . . . .+(1)/(2^(n)-1) , then

If a_(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+(1)/(5)+ . . . .+(1)/(2^(n)-1) , then

Statement -1: (1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+ . . . .+(n^(2))/((2n-1)(2n+1))=(n(n+1))/(2(2n+1)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)

Statement -1: (1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+ . . . .+(n^(2))/((2n-1)(2n+1))=(n(n+1))/(2(2n+1)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)

By using the principle of mathematical induction , prove the follwing : P(n) : 1/2 + 1/4 + 1/8 + ……..+ (1)/(2^n) = 1 - (1)/(2^n) , n in N