Home
Class 12
MATHS
For a positive integer n let a(n)=1+1/2+...

For a positive integer `n` let `a(n)=1+1/2+1/3+1/4+.....+1/((2^n)-1)dot` Then `a(100)lt=100` b. `a(100)dot> 100` c. `a(200)lt=100` d. `a(200)lt=100`

A

`a (100) lt 100`

B

`a (200 ) lt 200`

C

`a(200) gt 100`

D

`a(100) lt 200`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Promotional Banner

Similar Questions

Explore conceptually related problems

For a positive integer n let a(n)=1+1/2+1/3+1/4+.....+1/((2^n)-1)dot Then a(200)lt=100 b. a(200) > 100 c. a(200)lt=100 d. a(200)lt=100

The number of positive integers satisfying the inequality C(n+1,n-2) - C(n+1,n-1)<=100 is

If n is a positive integer, then prove that 81^n + 20 n - 1 is divisible by 100

If 1/5-1/6=4/x , then x= (a) -120\ (b) -100 (c) 100 (d) 120

Let a_n is a positive term of a GP and sum_(n=1)^100 a_(2n + 1)= 200, sum_(n=1)^100 a_(2n) = 200 , find sum_(n=1)^200 a_(2n) = ?

The number of positive integers satisfying the inequality C(n+1,n-2)-C(n+1,n-1)<=100 is

The number of positive intergers satisfying the in-equality ""^(n+1)C_(n-2)-""^(n+1)C_(n-1)le100 , is

If f(x)=1+x+(x^2)/2+...+(x^(100))/(100), then f^(prime)(1) is equal to a. 1/(100) b. 100 c. 50 d. 0

If 25^(n-1) + 100 = 5^ (2n-1) , find the value of n :

If S_(n) = 1 + (1)/(2) + (1)/(2^(2))+….+(1)/(2^(n-1)) , find the least value of n for which 2- S_(n) lt (1)/(100) .