Home
Class 12
MATHS
The sum of 0.2+0.004+0. 00006+0. 0000008...

The sum of `0.2+0.004+0. 00006+0. 0000008+...` to `oo` is

A

`200/891`

B

`2000/9801`

C

`1000/9801`

D

`2180/9801`

Text Solution

Verified by Experts

The correct Answer is:
D
`S=2/10+4/10^(3)+6/10^(5)+8/10^(7)+..` to `oo` (1)
`=(2/10)/(1-1/10^(2))+(2xx(1/10^(2)))/((1-1/10^(2))^(2))`
`=20/99+200/9801`
`=2180/9801`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise EXERCIESE ( LINKED COMPREHENSION TYPE )|60 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.9|9 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

Find value : (v) 0.04 × 0.04

Which term of this-progression 0.004, 0.02, 0.1..... is 12.5?

Find the sum to n terms : 0.7 + 0.77+0.777+….

The sum of first 20 term of the squence .7,0.77,0.777,… is -

Find the sum of the following series : 0. 7+0. 77+0. 777+ ton terms

Find the sum to indicated number of terms in each of the geometric progressions in 0.15, 0.015, 0.0015 ,.........20 terms .

The sum of first 20 terms of the sequence 0.7 , 0.77 , 0.777,... is

The sum of the distances of a moving point from the points (5 , 0 , 0) and ( - 5 , 0 , 0) is always 20 unit . Find the equation to the locus of the moving point .

CENGAGE PUBLICATION-PROGRESSION AND SERIES-EXERCIESE ( SINGLE CORRECT ANSWER TYPE )
  1. If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then valu...

    Text Solution

    |

  2. Find the sum of the series 1+4/5+7/(5^2)+10/(5^3)+...

    Text Solution

    |

  3. The sum of 0.2+0.004+0. 00006+0. 0000008+... to oo is

    Text Solution

    |

  4. The positive integer n for which 2xx2^2xx+3xx2^3+4xx2^4++nxx2^n=2^(n+1...

    Text Solution

    |

  5. If omega is a complex nth root of unity, then underset(r=1)overset(n)...

    Text Solution

    |

  6. about to only mathematics

    Text Solution

    |

  7. The 15th term of the series 2 1/2+1 7/(13)+1 1/9+(20)/(23)+.. is

    Text Solution

    |

  8. If a1, a2, ,an are in H.P., then (a1)/(a2+a3++an),(a2)/(a1+a3++an), ...

    Text Solution

    |

  9. If a1, a2, a3, an are in H.P. and f(k)=(sum(r=1)^n ar)-ak ,t h e n (a...

    Text Solution

    |

  10. If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a ...

    Text Solution

    |

  11. If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a ...

    Text Solution

    |

  12. a,b,c,d in R^+ such that a,b and c are in H.P and ap.bq, and cr are in...

    Text Solution

    |

  13. If in a progression a1, a2, a3, e t cdot,(ar-a(r+1)) bears a constant...

    Text Solution

    |

  14. If a,b, and c are in G.P then a+b,2b and b+ c are in

    Text Solution

    |

  15. If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that...

    Text Solution

    |

  16. Let n in N ,n > 25. Let A ,G ,H deonote te arithmetic mean, geometric...

    Text Solution

    |

  17. If A.M., G.M., and H.M. of the first and last terms of the series of 1...

    Text Solution

    |

  18. If H1.,H2,…,H20 are 20 harmonic means between 2 and 3, then (H1+2)/(H1...

    Text Solution

    |

  19. If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum o...

    Text Solution

    |

  20. If bi=1-ai ,n a=sum(i=1)^n ai ,n b=sum(i=1)^n bi ,t h e nsum(i=1)^n ai...

    Text Solution

    |