Home
Class 12
MATHS
The sum of 0.2+0.22+0.222+. . . . To n t...

The sum of 0.2+0.22+0.222+. . . . To n terms is equal to

A

`((2)/(9))-((2)/(81))(1-10^(-n))`

B

`n-((1)/(9))(1-10^(-n))`

C

`((2)/(9))[n-((1)/(9))(1-10^(-n))]`

D

`((2)/(9))`

Text Solution

Verified by Experts

The correct Answer is:
C
`S_(n)=0.2+0.22+0.022+ . . .` upto n terms
`=2[0.1+0.11+0.111+` upto n terms]
`=(2)/(9)[0.9+0.99+0.999+ . . ."upto n terms"] `
`=(2)/(9)[(1-0.1)+(1-(0.1)^(2))`
`+(1-(0.1)^(3))+. . ."upto n terms"]`
`=(2)/(9)[n-((0.1)+(0.1)^(2)+(0.1)^(3)"+. . . untp n terms")]`
`=(2)/(9)[n-(0.1)([1-(0.1)^(n)])/(1-0.1)]`
`=(2)/(9)[n-(1)/(9)[1-10^(-n)]]`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PRACTICE SET 03

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|49 Videos

  • PRACTICE SET 05

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

Similar Questions

Explore conceptually related problems

Find the sum of 2+0.2+0.02+0.002+... upto 20 terms

If in an A.P.the sum of m terms is equal of n and the sum of n terms is equal to m, then prove that the sum of -(m+n) terms is (m+n).

Knowledge Check

  • The sum of 0.2 + 0.22 + 0.222 +… upto n terms is equal

    A
    `(2/9)-(2/81)(1-10^(-n))`
    B
    `n-(1/9)(1-10^(-n))`
    C
    `(2/9)[n-(1/9)(1-10^(-n))`
    D
    `(2/9)`

  • 0.2 + 0.22 + 0.222 + … upto n terms is equal to

    A
    `((2)/(9)) - ((2)/(81)) (1-10^(-n))`
    B
    `n-((1)/(9))(1-10^(-n))`
    C
    `((2)/(9))[n-((1)/(9))(1-10^(-n))]`
    D
    `(2)/(9)`

  • What is the sum of the series 0.3+0.33+0.333+. . . .n terms ?

    A
    `(1)/(3)[n-(1)/(9)(1-(1)/(100^(n)))]`
    B
    `(1)/(3)[n-(1)/(9)(1-(1)/(10^(n)))]`
    C
    `(1)/(3)[n-(1)/(3)(1-(1)/(10^(n)))]`
    D
    `(1)/(3)[n-(1)/(9)(1+(1)/(10^(n)))]`

    • Similar Questions

    Explore conceptually related problems

    If the sum of the first n terms of a sequence is equal to √ (3/ 2) ( n^ 2 − n ) , then the sum of the squares of these terms is equal to

    If in an A.P.the sum of m terms is equal to n and the sum of n terms is equal to m then prove that the sum of (m+n) terms is -(m+n)

    If in an AP,the sum of m terms is equal to n and sum of n terms is equal to m.Then prove that sum of (m+n) terms is -(m+n)

    Sum of the series 0.5+0.55+0.555+.... upto n terms is

    Is the given sequence 0.2,0.22,0.222,...... form an A.P. ?

    Home
    Profile