Home
Class 12
MATHS
Find the sum of the series 1+2(1-x)+3(1-...

Find the sum of the series `1+2(1-x)+3(1-x)(1-2x)+….+n(1-x)(1-2x)(1-3x)….(1-(n-1)x)`

A

`S_(n) = -(1)/(x) [(1-x)(1-2x)"………"(1-nx)-1]`

B

`S_(n) = -(1)/(x) [(1-x)(1-2x)"………"(1-6x)-1]`

C

`S_(n) = (1)/(x) [(1-x)(1-2x)"………"(1-nx)-1]`

D

`S_(n) = (1)/(x) [(1-x)(1-2x)"………"(1-nx)-1]`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos
  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

If x is positive, the sum to infinity of the series 1/(1+x)-(1-x)/((1+x)^2)+(1-x) ^2/((1+x)^3)-(1-x)^3/((1+x)^4)+....... i s (a)1/2 (b) 3/4 (c) 1 (d) none of these

Find the sum of the series (1+2x+3x^(2)+(n-1)x^(n-2)) using differentiation.

Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiation.

Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiation.

Sum to n terms of the series (1)/((1 +x) (1 + 3x)) + (1)/( ( 1 + 3x) (1 + 5x)) + (1)/((1 + 5x ) (1 + 7x)) +…….

Find the sum of 20 terms of the series (x+(1)/(2))+(3x-(1)/(6))+(5x+(1)/(18))+....

Let n is a rational number and x is a real number such that |x|lt1, then (1+x)^(n)=1+nx+(n(n-1)x^(2))/(2!)+(n(n-1)(n-2))/(3!).x^(3)+ . . . This can be used to find the sm of different series. Q. The sum of the series 1+(1)/(3^(2))+(1*4)/(1*2)*(1)/(3^(4))+(1*4*7)/(1*2*3)*(1)/(3^(6))+ . . . . is

The sum of the series (1)/(1!)x+(2)/(2!)x^(2)+(3)/(3!)x^(3) ….. To infty is

The sum of the series (x-1)/(x+1)+1/2(x^(2)-1)/(x+1)^(2)+1/3(x^(3)-1)/(x+1)^(3) +…is equal to

Find the sum of the series 1+2^(2)x+3^(2)x^(2)+4^(2)x^(3)+"...."" upto "infty|x|lt1 .

RESONANCE ENGLISH-DPP-QUESTION
  1. Which one of the following inequality holds good:

    Text Solution

    |

  2. If x cos alpha+cos beta-cos(alpha+beta) and y=4 sin.(alpha)/(2)sin.(be...

    Text Solution

    |

  3. Find the sum of the series 1+2(1-x)+3(1-x)(1-2x)+….+n(1-x)(1-2x)(1-3x)...

    Text Solution

    |

  4. If a,b respectively be the number of solutions and sum of solutions of...

    Text Solution

    |

  5. The equation |x + 2| - |x + 1| + |x -1| =K,x in R has two solutions i...

    Text Solution

    |

  6. The "sum" of integral solutions of equations |sin^(2)x+17-x^(2)|=|16-x...

    Text Solution

    |

  7. solution set of the inequality sqrt(7-x) > 2x-3 , is contained by the ...

    Text Solution

    |

  8. a ,b ,c are positive real numbers forming a G.P. If ax^2+2b x+c=0 and ...

    Text Solution

    |

  9. Let y = cosx (cosx - cos 3x). Then y is

    Text Solution

    |

  10. The (m + 1)^(th) term of (x/y+y/x)^(2m + 1 ) is

    Text Solution

    |

  11. The remainder when 2^(2003) is divided by 17 is:

    Text Solution

    |

  12. Solution set of 4 sintheta*costheta-2 costheta-2sqrt3 sin theta+sqrt3 ...

    Text Solution

    |

  13. sin 36^(º)sin 72^(º) sin108^(º) sin 144^(º) =

    Text Solution

    |

  14. In an A.P. the third term is four times the first term, and the sixth ...

    Text Solution

    |

  15. The sum of three numbers in A.P. is 27, and their product is 504, find...

    Text Solution

    |

  16. Determine all pairs (a,b) of real numbers such that 10, a,b,ab are in ...

    Text Solution

    |

  17. Draw the graph of (i) y = |x+2| + |x-3| . (ii) y = x+(x)/(|x|)

    Text Solution

    |

  18. |(2x+1)/(x-1)| gt 2

    Text Solution

    |

  19. |x-1|+|x-2|+|x-3| ge 6

    Text Solution

    |

  20. Solve log(2)|x| lt 3

    Text Solution

    |