Home
Class 11
MATHS
Sum the series n+(n-1)x+(n-2)x^2+..........

Sum the series `n+(n-1)x+(n-2)x^2+.......+2x^(n-2)+x^(n-1)`.

Text Solution

Verified by Experts

`x((x^n-1))/(x-1)^2-n/(x-1)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

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

Find the derivative of x^(n)+ax^(n-1)+a^(2)x^(n-2)+…+a^(n-1)x+a^(n) for some fixed real number a.

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

From the relation 1+x+x^(2)+* * * + x^(n-1)=(1-x^(n))/(1-x) , find the sum of the series 1+2x+3x^(2)+* * * +(n-1)x^(n-2) .

Find the sum of the series .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1).^(n)C_(n)x^(n) and hence show that , .^(n)C_(0)+2.^(n)C_(1)x+3.^(n)C_(2)x^(2)+....+(n+1)^(n)C_(n)=(n+2)2^(n-1)

Show that the middle term in the expansion of (x+1)^(2n) is (1.3.5.....(2n-1))/(n!) 2^n.x^n .

Show that the middle term in the expansion of (x-1/x)^(2n) is (1.3.5.7....(2n-1))/(n!)(-2)^n

Sum of n terms of the series (2n-1)+2(2n-3)+3(2n-5)+.... is

Prove that the middle term in the expansion of (1+x)^(2n)" is " (1.3.5....(2n-1))/(n!).2^(n)x^(n)

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. Find the sum of n terms of series 1+5((4n+1)/(4n-3))+9((4n+1)/(4n-3))^...

    Text Solution

    |

  2. Find the sum of the products of the integers 1,2,3,....n taken two at ...

    Text Solution

    |

  3. Sum the series n+(n-1)x+(n-2)x^2+.......+2x^(n-2)+x^(n-1).

    Text Solution

    |

  4. Find 1+2^2x+3^2x^2+4^2x^3+.... to infty absx lt 1.

    Text Solution

    |

  5. Find the sum of 1st n terms of the sequence 3,6,15,42,123,...

    Text Solution

    |

  6. Let Sn denote the sum of first n terms of the sequence 1,5,14,30,55,.....

    Text Solution

    |

  7. Finds the sum of first n terms of the series 3/(1^2xx2^2)+5/(2^2xx3^2)...

    Text Solution

    |

  8. How many terms of the series 54+51+48+45+ ... must be taken to make 51...

    Text Solution

    |

  9. If (b+c),(c+a),(a+b) are in H.P. show that a^2 ,b^2 , c^2 are in A.P.

    Text Solution

    |

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

    Text Solution

    |

  11. If 0 < theta < pi/2 then find the least value of tantheta+cottheta

    Text Solution

    |

  12. If x and y are positive quantities whose sum is 4, show that (x+1/x)^2...

    Text Solution

    |

  13. If a,b,c gt 0 show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)le(a+b+c)/2.

    Text Solution

    |

  14. Show that a^2(1+b^2)+b^2(1+c^2)+c^2(1+a^2)ge6abc.

    Text Solution

    |

  15. If m, n are positive quantities, prove that ((mn+1)/(m+1))^(m+1)gen^m.

    Text Solution

    |

  16. Prove that ((bc+ac+ab)/(a+b+c))^(a+b+c)ge(b)^a(c)^b(a)^c [where a,b,c ...

    Text Solution

    |

  17. If log2,log(2^n-1) and log(2^n+3) are in A.P. then n =

    Text Solution

    |

  18. If the ratiio of the sum of n terms ofd two AP's is (3n+1):(2n+3) then...

    Text Solution

    |

  19. If a1,a2,a3,.......an are in AP where a1 gt 0foralli then the value of...

    Text Solution

    |

  20. Given p no. of A.P. each of which consists of an n terms. If their fir...

    Text Solution

    |