Wednesday, October 9, 2019

ordinary differential equations - why are these two power series the same



n=1ncnxn=n=0ncnxn



How come one starts at 1 and the other starts at 0 yet their equal?
Do they both equal infinity?



Answer



When n=0, ncnxn is also zero. So the first sum just leaves that zero term out while the second one includes it. There is no change in the sum.


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