Differentiating power series

  1. My question is just a concept that I don't understand.

    When differentiating a power series that starts at n=0 we bump that bound up to n=1.

    My question is do we always do that?

    or

    Do we only do that when the first term of the power series is a constant and thus when it is differentiated it becomes zero?

    My guess is the second case.
     
  2. jcsd
  3. Huh? n = 0 is just the index. We can call out "starting point" a0 or a1 --- whichever we prefer. And yes, that term will disappear when you take the derivative of ∑anxn.

    a0 + a1x + a2x2 + ...

    (a0 + a1x + a2x2 + ... )' = a1 + 2a2x + ...

    It's as simple as that.
     
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