" (n) "(1)/(2)+(1)/(4)+(1)/(8)+cdots+(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))

For all ninNN , prove by principle of mathematical induction that, (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))

For a positive integer n let a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)cdots+(1)/((2^(n))-1). Then a(100) 100c.a(200)<=100d.a(200)<=100

For a positive integer n, let a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+ . . .+(1)/(2^(n)-1) Then:

If S_(1), S_(2),cdots S_(n) , ., are the sums of infinite geometric series whose first terms are 1, 2, 3,…… ,n and common ratios are (1)/(2) ,(1)/(3),(1)/(4),cdots,(1)/(n+1) then S_(1)+S_(2)+S_(3)+cdots+S_(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)

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

The arithmetic mean of the series 1,2,4,8,16,....2^(n) is (2^(n)-1)/(n+1) (b) (2^(n)+1)/(n) (c) (2^(n)-1)/(n) (d) (2^(n+1)-1)/(n+1)