Home
Class 12
MATHS
If Sn = 1+1/2 + 1/2^2+...+1/2^(n-1) and ...

If `S_n = 1+1/2 + 1/2^2+...+1/2^(n-1) and 2-S_n < 1/100,` then the least value of `n` must be :

Text Solution

Verified by Experts

The correct Answer is:
8
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MATHEMATICS TIPS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|21 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise PARAGRAPH BASED (MULTIPLE CHOICE) (COMPERHENSION - XVI)|3 Videos

  • MATHEMATICS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|15 Videos

  • MATRICES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

If S_n=1+1/3+1/3^2+...+1/3^n-1, n in N , then least value of n such that 3-2 S_n lt 1/100 , is

Let S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4. The sum sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!)) is equal to :

Knowledge Check

  • Let S_n=1/1^2 + 1/2^2 + 1/3^2 +….. + 1/n^2 and T_n=2 -1/n , then :

    A
    `S_2 lt T_2`
    B
    If `S_k lt T_k` then `S_(k+1) lt T_(k+1)`
    C
    `S_n lt T_n AA n ge 2`
    D
    `S_n gt T_n AA n ge 2007`

  • Directions for questions : Select the correct answer from the given options. In the formula S_(n) = (n)/(2) {2a + (n-1) d} , make d as the subject. The following steps are involved in solving the above problem. Arrange them in sequential order. A (n-1) d = (2S_n)/( n) - 2a B Given, S_(n) = (n)/(2) [2 a + (n-1) d] rArr n [2a + (n-1) d]= 2S_(n) C rArr d = (2)/( n-1) [ (S_n)/( n) - a] D 2a + (n-1) d = (2S_n)/( n) .

    A
    DBAC
    B
    BDAC
    C
    ABDC
    D
    BDCA

  • If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then

    A
    `0`
    B
    `1`
    C
    `2`
    D
    `3`

    • Similar Questions

    Explore conceptually related problems

    Let S_n = 1 (n - 1) + 2. (n -2) + 3. (n - 3) +…+ (n -1).1, n ge 4. The sum sum_(n = 4)^oo ((2S_n)/(n!) - 1/((n - 2)!)) is equal to :

    If S_ (n) = (n* ( 2 n^ 2 + 9 n + 13 ))/ 6 ( S_ (n) = sum of first n terms of the sequence) then the value of ∑_ (i = 1)^(oo) 1/ ( r √ (S_ r − S_ (r − 1))

    If S=sum_(n=2)^oo (3n^2+1)/(n^2-1)^3 then 9/S=

    If S_(1),S_(2),S_(3),"…….",S_(2n) are the same of infinite geometric series whose first terms are respectively 1 , 2, 3,"…….", 2n and common ratio are respectively. 1/2, 1/3, '…..". (1)/(2n+1) .Find the value of S_(1)^(2) + S_(2)^(2) + "……" + S_(2n-1)^(2) .

    If H_n=1+1/2+…+1/n , then the value of S_n =1+3/2+5/3+….+(2n-1)/n is

    Home
    Profile