Home
Class 12
MATHS
If S(n) denotes the sum of n terms of a ...

If `S_(n)` denotes the sum of n terms of a G.P., whose common ratio is r, then `(r-1) (dS_(n))/(dr) = `

A

`(n-1)S_(n)`

B

`(n-1)S_(n)-nS_(n-1)`

C

`(n-1)S_(n)+nS_(n-1)`

D

`(n+1)S_(n)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|206 Videos

  • ELLIPSE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|172 Videos

Similar Questions

Explore conceptually related problems

Let S_(n) denote the sum of first n terms of an A.P. If S_(2n) = 3S_(n) , then the ratio ( S_(3n))/( S_(n)) is equal to :

Find the sum to n terms of the A.P., whose k^("th") term is 5k + 1.

Let S_(n) denote the sum of the first n terms of an A.P. If S_(2n) = 3S_(n) , then S_(3n) : S_(n) is equal to :

Find the sum of n terms of the series whose nth terms is (i) n(n-1)(n+1) .

Find the sum of n terms of the series whose nth terms is (ii) n^(2)+3^(n) .

Find the sum to n terms of the series whose n^(th)" terms is n"(n+3) .

If S_(n)=(1)/(6) n(n+1)(n+2) is the sum to n terms of a series whose n^(th) term is T_(n) , then lim _(n rarr oo) sum_(r=1)^(n) (1)/(T) is

Find the sum to n terms of the series in whose n^(th) terms is given by n(n+1)(n+4)

HIMALAYA PUBLICATION-DIFFERENTIATION-QUESTION BANK
  1. If x = sqrt((1-t^(2))/(1+t^(2)) and y = (sqrt(1+t^(2))-sqrt(1-t^(2)))...

    Text Solution

    |

  2. If y = x+e^(x), then (d^(2)y)/(dx^(2)) is equal to

    Text Solution

    |

  3. If S(n) denotes the sum of n terms of a G.P., whose common ratio is r,...

    Text Solution

    |

  4. y = 1/(1+x^(beta-alpha)+x^(gamma-alpha))+ 1/(1+x^(alpha-beta)+x^(gamma...

    Text Solution

    |

  5. If y = (1+x^(1/4))(1+x^(1/2))(1-x^(1/4)), then dy/dx =

    Text Solution

    |

  6. If f(x) = x sin x, then f^(')(pi/2) is equal to

    Text Solution

    |

  7. Let f(x) = x-[x], x in R then f^(')(1/2) is

    Text Solution

    |

  8. If y = sqrtx + 1/x then dy/dx at x = 1 is

    Text Solution

    |

  9. If f(x) = (x-1)(x-2)(x-3), then f^(')(0) =

    Text Solution

    |

  10. If y = (1+1/x^(2))/(1-1/x^(2)) then dy/dx is

    Text Solution

    |

  11. If y = ((sin x + cos x)/(sin x - cos x)) then dy/dx at x = 0 is

    Text Solution

    |

  12. If y=("sin(x+9))/(cosx), then (dy)/(dx) at x=0 is :

    Text Solution

    |

  13. If f(x) = 1+x + x^(2)/2 + …. + x^(100)/100, then f^(')(1) is equal to

    Text Solution

    |

  14. If f(x)=(x^(n)-a^(n))/(x-a) for some constant 'a', then f'(a) is :

    Text Solution

    |

  15. If f(x) = x^(100) + x^(99) + ….+x + 1, then f^(')(1) is equal to

    Text Solution

    |

  16. If f(x) = 1-x + x^(2) - x^(3) + …. - x^(99) + x^(100), then f^(')(1) i...

    Text Solution

    |

  17. Differential coefficient of sec(tan^(-1) x) is

    Text Solution

    |

  18. If u=sin^(-1)((2x)/(1+x^(2))) and v=tan^(-1)((2x)/(1-x^(2))), then (du...

    Text Solution

    |

  19. The set of points where the function f given by f(x) = |x-3| cos x is ...

    Text Solution

    |

  20. The set of points where the function f given by f(x) = |2x-1|sin x is ...

    Text Solution

    |