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Is this a correct way to rewrite the binomial theorem?

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data
    I am doing a poof and I need to use the binomial theorem. However is the following a correct way to rewrite it?

    [tex](a+b)^n\ =\ {n \choose 0}a^{n} + \sum_{k=1}^{n}{n \choose k}\ a^{n-k}\ b^{k} [/tex]

    2. Relevant equations

    [tex](a+b)^n\ =\ \sum_{k=0}^{n}{n \choose k}\ a^{n-k}\ b^{k} [/tex]

    3. The attempt at a solution
    Basically, I want to extract the first term of the binomial expansion out of the summation but I'm not that good with sigma notation. Don't I just have to increase the lower bound by 1 and write the first term outside (as shown above)? Thanks.
     
  2. jcsd
  3. Mar 10, 2012 #2

    tiny-tim

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    hey jey1234! :wink:

    yes, that's fine :smile:
     
  4. Mar 10, 2012 #3
    thanks tim. one more quick question. is the following correct?

    [tex]\frac{1}{a}\sum_{k=1}^{n}a^{k}\ b^{k}\ =\ \sum_{k=1}^{n}a^{k-1}\ b^{k}[/tex]
     
  5. Mar 10, 2012 #4

    SammyS

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    Yes, that's correct.
     
  6. Mar 10, 2012 #5
    thanks sammy :smile:
     
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