Let and ... for x in R.

Prove that s' = c and c' = s.

I think you are supposed to differentiate term by term but i'm not sure exactly how that is done.

Thanks

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- November 3rd 2007, 07:56 PMtbyou87Differentiation of Power Series
Let and ... for x in R.

Prove that s' = c and c' = s.

I think you are supposed to differentiate term by term but i'm not sure exactly how that is done.

Thanks - November 3rd 2007, 07:59 PMThePerfectHacker
- November 3rd 2007, 08:00 PMJhevon
- November 3rd 2007, 08:49 PMtbyou87
So the first one makes sense to me.

I'm guessing for part b and c we are still using differentiation term by term. I guess i'm not seeing how to group them together so that they equal 0 for b and 1 for c.

Thanks - November 3rd 2007, 08:52 PMJhevon
- November 3rd 2007, 09:04 PMJhevon
ah! i remember the short way

since you (should have, by now) proved that it means that for some constant.

indeed, since the series and work for all , we have that the constant is the same for all . in particular, try and the conclusion is immediate