Home
Class 11
MATHS
Find the sum of the series 1*n+2*(n-1)+3...

Find the sum of the series `1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n*1` also, find the coefficient of `x^(n-1)` in th cxpansion of `(1+2x+3x^(2)+"...."nx^(n-1))^(2)`.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|435 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE|226 Videos

  • SETS

    MODERN PUBLICATION|Exercise EXERCISE|381 Videos

Similar Questions

Explore conceptually related problems

Find the sum of the series (1^(2)+1)1!+(2^(2)+1)2!+(3^(2)+1)3!+ . .+(n^(2)+1)n! .

Find the (n+1)th term from the end in the expansion of (2x - (1)/(x))^(3n)

Prove that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+x)^(2n-1)

Show that the coefficient of x^n in the expansion of (1+x)^(2n) is twice the coefficient of x^n in the expansion of (1+ x)^(2n-1) .

In the expansion of (x^(2) + 1 + (1)/(x^(2)))^(n), n in N ,

Find the value of n , if (2n - 1)/(n - 2) = 3

Prove that the coefficient of x^(n) in (1+x)^(2n) is twice the coefficient of x^(n) in (1+x)^(2n-1)

Find the sum of n terms of the series whose nth term is : 2^(n+1)+4(n+1)(n-2) .

Find the sum of the following series : 1.3.5+2.4.6 +3.5.7 + .... to n(n+2)(n+4) .

The coefficient of x^n , where n is any positive integer, in the expansion of (1+2x+3x^2 +... to oo)^(1//2) is:

MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. A manufacturer reckons that the value of a machine, which costs him Rs...

    Text Solution

    |

  2. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  3. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n...

    Text Solution

    |

  4. Find the sum of n terms\ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+do...

    Text Solution

    |

  5. Obtain the sum of the series : 1/1.4+1/4.7+1/7.10 + .......... to n t...

    Text Solution

    |

  6. Find the sum of n terms of the series (1)/(1+1^(2)+1^(4))+(2)/(1+2^(2)...

    Text Solution

    |

  7. Show that : (1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. ...

    Text Solution

    |

  8. What will Rs 500 amounts to in 10 years after its deposit in a bank wh...

    Text Solution

    |

  9. A man deposited ₹ 10,000 in a bank at the rate of 5% simple interest a...

    Text Solution

    |

  10. If a, b, c are in A.P. then 3^a, 3^b, 3^c are in:

    Text Solution

    |

  11. If the third term of an A.P is 12 and the seventh term is 24, then the...

    Text Solution

    |

  12. If a, b, c, d, e,f are in A.P., then e - c is equal to

    Text Solution

    |

  13. The third term of a GP is 3. What is the product of the first five ter...

    Text Solution

    |

  14. 5th term of a G.P. is 2, then the product of first 9 terms is:

    Text Solution

    |

  15. If the pth , qth , rth , terms of a GP . Are x,y,z respectively prove ...

    Text Solution

    |

  16. The sum of the first n odd number is :

    Text Solution

    |

  17. If the sum of n natural numbers is one sixth of their squares, then n ...

    Text Solution

    |

  18. The sum of the numbers 1, 4, 9, 16, ... , 100 is :

    Text Solution

    |

  19. If p, q, r are in A.P. while x, y, z are in G.P., prove that x^(q-r).y...

    Text Solution

    |

  20. If a^x=b^y=c^z and a, b, c are in G.P. then x,y,z are in :

    Text Solution

    |