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Differentiating power series

by EV33
Tags: differentiating, power, series
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EV33
#1
Jan18-11, 02:15 AM
P: 196
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.
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Jamin2112
#2
Jan18-11, 02:47 AM
Jamin2112's Avatar
P: 910
Quote Quote by EV33 View Post
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.
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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