Home
Class 12
MATHS
Two distinct, real infinite geometric se...

Two distinct, real infinite geometric series each have a sum of 1 and have the same second term. The third term of one of the series is `1/8`. If the second term of both the series can be written in the form `(sqrtm-n)/p` where m,n and p are positive integers and m is not divisible by the square of any prime, find the value of `100m + 10n + p`.

Text Solution

Verified by Experts

518
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -3 Subjective /JEE Advanced (Comprehension )|3 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -I Previous Year /JEE Main|19 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -2 (Level -II) Multiple Correct /JEE Advanced|9 Videos

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)|25 Videos

  • SOLUTION OF TRIANGLE

    MOTION|Exercise EXERCISE - 4( LEVEL II)|10 Videos

Similar Questions

Explore conceptually related problems

The nth term of a series is 3^(n)+2n; find the sum of first n terms of the series.

If the sum of the first n terms of the series

The sum of an infinite geometric series is 15 and the sum of the squares of these terms is 45.Find the series.

The sum of an infinite geomwtric series is 20 and the sum of the squares of these terms is 100. Find the series.

The first term of an infinite geometric series is 21. The seconds term and the sum of the series are both positive integers. The possible value(s) of the second term can not be

Find the sum to n term of the series whose nth term is n(n+1)(n+4)

In an increasing geometric series, the sum of the first and the sixth term is 66 and the product of the second and fifth term is 128 . Then the sum of the first 6 terms of the series is:

MOTION-SEQUENCE & SERIES -Exercise -3 Subjective /JEE Advanced
  1. The sum of first ten terms of an A.P. is 155 and the sum of first two ...

    Text Solution

    |

  2. In a set of four number, the first three are in GP & the last three ar...

    Text Solution

    |

  3. Find the 4^(th) term of an H.P., whose 7^(th) term is 1/20 and 13^(th)...

    Text Solution

    |

  4. Find the sum of the n terms of the series whose nth term is (i) n(n+...

    Text Solution

    |

  5. Find the sum of the series (5)/(13)+(55)/(13)^2+(555)/(13)^2+(5555)/((...

    Text Solution

    |

  6. If the expression exp {1+|cosx|+cos^(3)x|+cos^(4)x+ . . . . oo)log(e...

    Text Solution

    |

  7. The sum of the infinite series , 1^2- 2^2 / 5+ 3^2 / 5^2 - 4^2 / 5^3 +...

    Text Solution

    |

  8. Find the sum of the n terms of the sequence 1/(1+1^2+1^4)+2/(1+2^2+2^...

    Text Solution

    |

  9. Find the sum of the first n terms ofthe sequence : 1+2(1+1/n)+3(1+1/n)...

    Text Solution

    |

  10. Find the n term and the sum to n terms of the sequence: (i) 1+5+13+29+...

    Text Solution

    |

  11. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

    Text Solution

    |

  12. If a1,a,a3...an are in A.P then prove that a1^2-a2^2+a3^2-a4^2+....a(2...

    Text Solution

    |

  13. If a, b, c, d, e be 5 numbers such that a, b, c are in AP, b, c, d, ar...

    Text Solution

    |

  14. Using the relation A.M ge G.M. Prove that (i) tan theta +cot theta g...

    Text Solution

    |

  15. Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c), where a,b,c gt 0 .

    Text Solution

    |

  16. The arithmetic mean of two numbers is 6 and their geometric mean G and...

    Text Solution

    |

  17. In a circle of radius R a square is inscribed, then a circle is inscri...

    Text Solution

    |

  18. 9. Find three numbers a,b,c between 2 & 18 such that; (G) their sum is...

    Text Solution

    |

  19. Two distinct, real infinite geometric series each have a sum of 1 and ...

    Text Solution

    |

  20. One of the roots of the equation 2000x^6 +100x^5 +10x^3+x-2=0 is the f...

    Text Solution

    |