Home
Class 12
MATHS
The sum of 0.2 +0.22+0.222+ … to n ter...

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
` = 0.2 +0.22+0.222 +…` up to n terms
` = 2 [ 0.1 +0.11 +0.111+…" up to n terms"` ]
` = 2/9 [ 0.9 + 0.99 + 0.999 + ..." up to n terms" ]`
` = 2/9 [ (1-0.1)+(1-0.1)^(2) +(1-0.1)^(3)+..." up to n terms " `
` =2/9 [ n-(0.1)+(0.1)^(2)+(0.1)^(3) +... "up to 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

  • SEQUENCES AND SERIES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 9|1 Videos

  • SEQUENCES AND SERIES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 10|1 Videos

  • SEQUENCES AND SERIES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 7|1 Videos

  • PROBABILITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|4 Videos

  • SETS, RELATIONS AND FUNCTIONS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Exercise 2 (MISCELLANEOUS PROBLEMS)|30 Videos

Similar Questions

Explore conceptually related problems

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).

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)

Knowledge Check

  • 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)`

  • 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)`

  • If the sum to 2n terms of an Ap 2,5,8,11 , …. is equal to the sum to n terms of an AP 57,59,61,63, …. , then n is equal to

    A
    10
    B
    11
    C
    12
    D
    13

    • 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

    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 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 the arithmetic progression whose common difference is nonzero the sum of first 3n terms is equal to the sum of next n terms.Then,find the ratio of the sum of the 2n terms to the sum of next 2n terms.

    The sum of :3.^(n)C_(0)-8.. upto (n+1) terms is (n>=2):

    Home
    Profile