1300 Math Formulas

(Dana P.) #1
CHAPTER 11. SERIES


  1. o~Çáìë=çÑ=`çåîÉêÖÉåÅÉ=
    fÑ=íÜÉ=áåíÉêî~ä=çÑ=ÅçåîÉêÖÉåÅÉ=áë==(ñM−oIñM+o)==Ñçê==ëçãÉ=
    o≥MI=íÜÉ=o=áë=Å~ääÉÇ==íÜÉ=ê~Çáìë=çÑ=ÅçåîÉêÖÉåÅÉK==fí=áë=ÖáîÉå=
    ~ë=


å å~å

N


o äáã
→∞
= =çê=
åN

å
å ~

~


o äáã
→∞ +

= K==


=


=


=


11.9 Differentiation and Integration of Power


Series


=


`çåíáåìçìë=ÑìåÅíáçåW=Ñ=(ñ)

mçïÉê=ëÉêáÉëW=∑



å=M

å
~=åñ

tÜçäÉ=åìãÄÉêW=å=
o~Çáìë=çÑ=`çåîÉêÖÉåÅÉW=o=
=
=


  1. aáÑÑÉêÉåíá~íáçå=çÑ=mçïÉê=pÉêáÉë=


iÉí= ()=∑ = + + +K



=

O
M N O
åM

å
Ñ=Ñçê=ñ ~åñ ~ ~ñ ~ñ ñ<oK==

qÜÉåI==Ñçê=ñ<oI=Ñ(ñ)=áë=ÅçåíáåìçìëI=íÜÉ=ÇÉêáî~íáîÉ=Ñ′()ñ =
Éñáëíë=~åÇ=
′()= M+ N + ~OñO+K
Çñ

Ç



Çñ

Ç


~


Çñ

Ç


Ñ=ñ



=

= + + + = −


åN

åN
å

O
~N O~Oñ P~Pñ K å~ñ K=

=
=
=
Free download pdf