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
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    BITSAT GUIDE|Exercise BITSAT ARCHIVES|18 Videos
  • RECTANGULAR COORDINATES AND STRAIGHT LINE

    BITSAT GUIDE|Exercise BITSAT ARCHIVES|16 Videos
  • SETS, RELATIONS AND FUNCTIONS

    BITSAT GUIDE|Exercise BITSAT Archives|19 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)

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):

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

If the sum of the first 11 terms of an arithmetical progression equals that of the first 19 terms,then the sum of its first 30 terms,is (A) equal to 0 (B) equal to -1 (C) equal to 1 (D) non unique

BITSAT GUIDE-SEQUENCES AND SERIES -BITSAT ARCHIVES
  1. If p, q, r and s are positive real numbers such that p+ q + r + s = 2,...

    Text Solution

    |

  2. Sum of the series 1 + 2.2 + 3.2^(2) + 4.2^(3)+…+ 100.2^(99) is

    Text Solution

    |

  3. Find the sum to n terms of the series 5 + 55 + 555 + ...

    Text Solution

    |

  4. If a, b c are in GP and a^((1)/(x)) =b^((1)/(y)) =c^((1)/(z)), then x...

    Text Solution

    |

  5. The sum of the first n terms of the series (1)/(2)+(3)/(4)+(7)/(8)+(15...

    Text Solution

    |

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

    Text Solution

    |

  7. If AM and HM between two numbers are 27 and 12 respectively, then thei...

    Text Solution

    |

  8. The value of (2)/(1!) + (2+4)/(2!) + (2+4+6)/(3!) + … is

    Text Solution

    |

  9. IF a(1),a(2),a(3),"...."a(10) be in AP and h(1),h(2),h(3),"...."h(10) ...

    Text Solution

    |

  10. Let n is a rational number and x is a real number such that |x|lt1, th...

    Text Solution

    |

  11. The HM of two numbers is 4. If their arithmetic mean A and geometric m...

    Text Solution

    |

  12. For any integer n ge 1, the sum sum(k=1)^(n) k (k + 2) is equal to

    Text Solution

    |

  13. In DeltaABC, if (1)/(b+c)+(1)/(c+a)=(3)/(a+b+c), then C is equal to

    Text Solution

    |

  14. What is the sum of n terms of the series sqrt(2)+sqrt(8)+sqrt(18)+sqrt...

    Text Solution

    |

  15. Find the sum of the series 1 . 3^(2) + 2.5 ^(2) + 3.7^(2) +…+ to n t...

    Text Solution

    |

  16. If a = log(2)3, b = log(2) 5 and c = log(7)2, then log(140) 63 in term...

    Text Solution

    |

  17. When 2^(31) is divided by 5 the remainder is

    Text Solution

    |

  18. Let alpha, beta, gamma and delta be four positive real numbers such t...

    Text Solution

    |