You didn't use the hint
Notice that
But now by the hint we know this is a geometric series and gives
But we want the power series for f not its derivative so lets integrate to get
This gives
and since
Hi there. I have this exercise which I'm trying to solve now. It says:
Using that find one Taylor development for the function
So, I've made some derivatives:
And then:
I have two problems with this. In the first place, the general expression that I've found (which is probably wrong) doesn't work for n=0, it does for the others values of n. I thought of starting the summation at 1, but I'm not sure if this is valid. In the second place I don't know how to use the relation the problem gives at the beginning. I can see that I have (1-x_0) for every term, but I couldn't make it fit inside the summation.
So this is what I got:
Bye there, thanks for your help and suggestions.
Thank to all of you. Now I'm trying to solve the same exercise, but with the function I've tried to make some algebraic work to get the expression I'm looking for, but I didn't get it.
I've made the first derivative, and a few more, but I think its just necessary the first, as before. I get:
I thought of making
So, when I take the derivative in this last form I get:
I'm not sure how to proceed.