Home
Class 12
MATHS
it is known for x ne 1 that 1+x+x^(2)+"…...

it is known for `x ne 1` that `1+x+x^(2)+"….."+x^(n-1) = (1-x^(n))/(1-x)`, hence find the sum of the series `S = 1+2x+3x^(2)+"….."+(n+1)x^(n)`.

Text Solution

Verified by Experts

The correct Answer is:
`((n+1)x^(n+2)-(n+2)x^(n+1)+1)/((1-x)^(2))`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

Find the sum of the series 1+3x+5x^(2)+7x^(2)+... to n terms.

Find the sum to n terms of the series: 1+2x+3x^(2)+4x^(3)+......

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.

Show that 1+2x + 3x^2 +….+ nx^(n-1) = (1-(n+1)x^(n) + nx^(n+1))/((1-x)^2) for all n in N .

Find the sum to n terms of the series n+(n-1)x+(n-2)x^(2)+.........+2x^(n-2)+x^(r)

In the expansion of (1 + x) (1 + x+ x^(2)) …(1 + x + x^(2) +… +x^(2n)) , the sum of the coefficients is

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

RESONANCE-DPP-QUESTION
  1. The number of zeros at the end of 70!, is

    Text Solution

    |

  2. The coefficient of x^5in(1+2x+3x^2+)^(-3//2)i s(|x|<1) 21 b. 25 c. 26...

    Text Solution

    |

  3. it is known for x ne 1 that 1+x+x^(2)+"….."+x^(n-1) = (1-x^(n))/(1-x),...

    Text Solution

    |

  4. Match the following :

    Text Solution

    |

  5. The are enclosed by 2|x|+3|y| le 6 is

    Text Solution

    |

  6. A possible three digit even number which can be formed with the condit...

    Text Solution

    |

  7. The number of different seven digit numbers that can be written using ...

    Text Solution

    |

  8. Number of natural numbers between 100 & 1000 such that at least one of...

    Text Solution

    |

  9. A class contains 4 boys and g girls. Every Sunday five students, inclu...

    Text Solution

    |

  10. Let A,B,C,D be collinear points in that order. Suppose AB: CD = 3:2 an...

    Text Solution

    |

  11. If A & B are the points (-3,4)a n d(2,1) , then the co-ordinates of th...

    Text Solution

    |

  12. If in triangle A B C ,A-=(1,10), circumcentre -=(-1/3,2/3) and orthoce...

    Text Solution

    |

  13. If the 6th term in the expansion of [1/x^(8/3)+x^2 log10 x]^8 is 5600...

    Text Solution

    |

  14. If the second term of the expansion [a^(1/(13))+a/(sqrt(a^(-1)))]^n is...

    Text Solution

    |

  15. The co-efficient of x in the expansion of (1-2x^3+3x^5)(1+1/x)^8 is:

    Text Solution

    |

  16. If (1!)^(2) + (2!)^(2) + (3!)^(2) + "…….." + (99!)^(2) is divided by 1...

    Text Solution

    |

  17. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

    Text Solution

    |

  18. STATEMENT - 1 : The term independent of x in the expansion of (x+1/x+2...

    Text Solution

    |

  19. If roots of the equation x^2-2ax+a^2+a-3=0 are real and less than 3 t...

    Text Solution

    |

  20. A dictionary is made of the words that can be the position of the word...

    Text Solution

    |