@janhardo 

i bought years back some used calculus books : thomas calculus, early trancedentals and another calculus book

There is lot to find there in those books about powerseries, so i  want to dive further with Maple in the powerseries...  

@Carl Love 

Thanks

There is a lot to say more about this converge of powerseries  
-  d'Alembert 
-  Cauchy 
 

A dutch example https://www.hhofstede.nl/modules/machtreeksen.htm

A question here  : Why is such convergence area  in fact always symmmetrical with middle a ( waarom is zo'n convergentiegebied.... )

Well this goes too far for me to investigate 
  

@acer 

Thanks 

Some handy properties of powerseries: 

•  by summing or multiplication of two powerseries around x = a you get a new powerseries around x = a  with as radius of convergence the smallest of the original convergence radiusses.
•  by differentation or integration of a powerseries the radius of convergense keeps preserved. 

@Carl Love 

Thanks

With this clear example i can try to answer  other  series tasks     

@janhardo 

The posts are crossing
Note: its my interest in series that i zoom in on the task in the programming book how series can be related with eachother.

@vv 

Thanks

I don't know what the solutions strategy is yet ?

Download uitwerkingvraagbeatwioording_forum.mw

@vv 

Thanks 

As i understand it correct : S series is included in F series. 
But there is a given series S and how  to know at forehand that series F is related with series S ?

@Carl Love 

Thanks 

I am puzzling on the first book example for a given sum  how this to get  by  a integral.
Yes, there is studymaterial about power series. 

Seems to be useful infinite series handling, probably in further programming tasks? 

Is there a connection between of a function with his:   derative, integral and serie ?

@Carl Love 

Thanks

Yes, i understand it that you mention it for completeness.

Complex analyse is not that easy as it is for real numbers.

@acer 

Thanks, indeed this question has nothing to do with complex numbers and know nothing about complex functions

 

@Carl Love 

Thanks

I do have  some basic understanding of complex numbers, but complex functions( analyse) i did not yet studied.
 

@Carl Love 

Thanks
I did 

convert(ln(1+x),FPS); and get 

 Sum((-1)^k*x^(k + 1)/(k + 1), k = 0 .. infinity)  = 

But value(sum((-1)^k*x^(k + 1)/(k + 1), k = 0 .. infinity)); gives back again 

So f(x)= ln(1+x)   gives a serie, but this serie gives not the function back
Domain is < 0 to ? from ln(1+x)  and serie start at x = 0
It must be functions what their domain ranges from 0 ...n  to get from a serie a function back then?   

Don't know how to handle this vectorvalued function task for 4 points with tangentlines (or velocity lines?) and accelleration lines 

There was a task made  with a parametric curve also with 3 points and tangentlines, but the vectornotation differs
I tried task 8(i) for curve see post

I choose 4 points from t = 0 ,1/4 , 1/2, 3/4  (they must no too close and interesting )

blz35.pdf

blz36.pdf

hfdts2_blz37.pdf

@vv 

Thanks

Is it possible to get a function from a FPS serie ?