Do we always bump the bound up to n=1 when differentiating a power series?

[EV33]

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.

 

[Jamin2112]

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 ∑a_nxⁿ.

a₀ + a₁x + a₂x² + ...

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

It's as simple as that.