Hello. I just wanted to figure out why the lower bounds change when differentiating or integrating power series and is there a general rule to follow to know what that lower bound changes to?
#calculus 2 power series bounds change
reef mortar
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Hello. I just wanted to figure out why the lower bounds change when differentiat...
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lone harbor
Hello. I just wanted to figure out why the lower bounds change when differentiat...
If you're talking about how, for instance, d/dx sum(n = 0, inf) x^n = sum(n = 1, inf) nx^(n - 1), you aren't necessarily "changing the bounds". Here's what's happening in full detail: d/dx sum(n = 0, inf) x^n = sum(n = 0, inf) d/dx x^n = sum(n = 0, inf) nx^(n - 1) = 0 * x^(-1) + sum(n = 1, inf) nx^(n - 1) = sum(n = 1, inf) nx^(n - 1)See, we didn't reindex, we just pulled out a term that equalled zero.