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Im currently in a Calc II class with unfortunately a bad professor (score of 2 on RateMyProfessor), so I often have to resort to outside sources to learn. Our class is currently on Sequences and Series which has been fine up until we hit the topic of relating Power Series and Functions.

Example: ∑ x^n = 1/(1-x) when |x|<1

Now we receive weekly homework assignments, our prof went over differentiation and integration of power series VAGUELY with a few examples that don't help. So naturally I turned to the internet for help, whilst going through source after source that apparently is explaining this stuff, I can comfortably say that I have no idea what is going on in problems such as this.

f(x) = ∑((1)/((4^n)(n^2))(x-1)^n

x

Find ∫ f(t)dt As a series. Then find the Interval of Convergence

1

I actually don't even know where to start, so if anyone can offer any sort of insight into these types of problems I would be grateful.

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# Why can no one explain Power Series and Functions clearly

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