Results 1 to 4 of 4

Thread: Power rule.

  1. #1
    Newbie BraveHeart's Avatar
    Joined
    Jan 2010
    Posts
    5

    Power rule.

    Prove that:

    \displaystyle{\left(\sum_{k=0}^{n}a_{k}x^{k}\right  )' = \sum_{k=1}^{n}ka_{k}x^{k-1}}

    and/or that

    \int\left(\sum_{k=0}^{n}a_{k}x^{k}\right){dx} = \sum_{k=0}^{n}\frac{a_{k}x^{k+1}}{k+1}+c
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    I'm feeling an induction proof coming on. It's not like they are infinite sums. You won't have to worry about convergence.

    Maybe I'm wrong.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    18,188
    Thanks
    2424
    No, completely right. Induction on n and the "sum rule": (f(x)+ g(x))'= f'(x)+ g'(x).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie BraveHeart's Avatar
    Joined
    Jan 2010
    Posts
    5
    I'm not sure how to proceed with induction.

    Because \left(\sum_{k=0}^{n}a_{k}x^{k}\right)' = \sum_{k=0}^{n}\left(a_{k}x^{k}\right)' = \sum_{k=0}^{n}a_{k}\left(x^{k}\right)', what needs to be proven is that \left(x^{k}\right)' = kx^{k-1}. The same goes to \int\left(\sum_{k=0}^{n}a_{k}x^{k}\right){dx}<br />
.
    Last edited by BraveHeart; Feb 10th 2010 at 09:35 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Reciprocal Rule to verify the Power Rule
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Feb 11th 2011, 10:08 AM
  2. The power rule
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 11th 2009, 07:03 AM
  3. Power Rule
    Posted in the Calculus Forum
    Replies: 12
    Last Post: Mar 2nd 2009, 03:49 PM
  4. Chain Rule, and Power Rule
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Sep 23rd 2008, 11:00 AM
  5. Replies: 2
    Last Post: Dec 13th 2007, 05:14 AM

Search Tags


/mathhelpforum @mathhelpforum