Asked by Anon
Sum(n=1 to infinity) ((2x+5)^n) / (n(4^n))
Can someone write out the steps to finding the center point for this power series?
Can someone write out the steps to finding the center point for this power series?
Answers
Answered by
Steve
The series
∑a<sub><sub>n</sub></sub> (x-c)<sup><sup>n</sup></sup> has center at x=c
So, how do we massage your series into that form?
2x+5 = 2(x + 5/2)
So, your sum now is just like
2/(n*4^n) (x + 5/2)<sup><sup>n</sup></sup>
The center is at x = -5/2
∑a<sub><sub>n</sub></sub> (x-c)<sup><sup>n</sup></sup> has center at x=c
So, how do we massage your series into that form?
2x+5 = 2(x + 5/2)
So, your sum now is just like
2/(n*4^n) (x + 5/2)<sup><sup>n</sup></sup>
The center is at x = -5/2
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