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In this video I recap on term-by-term differentiation and integration of power series. This theorem, which I proved in my earlier video, states that the derivative of a power series is equivalent to first taking the derivative of each term and then summing it up. Likewise this is true for integrating a power series as well. In both cases, the radius of convergence is the same as that of the original power series. Note that the interval of convergence need not be the same for either case. Differentiating power series term-by-term has an important application in solving differential equations so make sure you fully grasp this concept!
The timestamps of key parts of the video are listed below:
This video was taken from my earlier video listed below:
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