How Can Power Series Help You Solve Complex Equations?

Click For Summary
SUMMARY

The discussion focuses on solving complex equations using power series, specifically the power series for ln(5 - x). The correct approach involves integrating the series for 1/(5 - x) rather than differentiating it. This method is essential for accurately deriving the power series representation of the logarithmic function. Participants emphasize the importance of understanding the relationship between differentiation and integration in power series applications.

PREREQUISITES
  • Understanding of power series and their convergence
  • Knowledge of integration techniques in calculus
  • Familiarity with the function ln(x) and its properties
  • Basic skills in manipulating series and sequences
NEXT STEPS
  • Study the derivation of power series for common functions, including ln(x)
  • Learn about the relationship between differentiation and integration in series
  • Explore convergence tests for power series
  • Practice solving complex equations using power series methods
USEFUL FOR

Students in calculus, mathematicians, and anyone looking to deepen their understanding of power series and their applications in solving complex equations.

sai2020
Messages
26
Reaction score
0

Homework Statement



See the attached png


Homework Equations



See the attached png

The Attempt at a Solution



See the attached png
 

Attachments

  • Picture 1.png
    Picture 1.png
    18.7 KB · Views: 501
Physics news on Phys.org
Well, it looks like you're trying to find the power series of ln(5 - x) by differentiating the series for 1/(5 - x) term by term. But ln(5 - x) is the integral of 1/(5 - x) (give or take a sign).
 
In other words integrate, don't differentiate!
 
Oh. how stupid am i. God help me in my exam.
 

Similar threads

Solving the Fourier cosine series
  • · Replies 1 ·
Replies
1
Views
2K
Finding the Fourier cosine series for ##f(x)=x^2##
  • · Replies 4 ·
Replies
4
Views
2K
How do I solve the Laplace equation using Robbin's Boundary Conditions?
  • · Replies 3 ·
Replies
3
Views
2K
Solving a Problem: Have I Made a Mistake or Are the Solutions Wrong?
  • · Replies 4 ·
Replies
4
Views
1K
How Do You Find the Limit of the Series S_n = \dfrac {3}{8}⋅\dfrac {4^n}{3^n}?
  • · Replies 2 ·
Replies
2
Views
1K
Linear operator in 2x2 complex vector space
  • · Replies 18 ·
Replies
18
Views
3K
Solve for ##x## in an equation involving surds
  • · Replies 8 ·
Replies
8
Views
2K
Calculus 1 problems: functions, integrals, series
  • · Replies 3 ·
Replies
3
Views
2K
Discussing the Convergence of a Series: Get My Opinion!
  • · Replies 4 ·
Replies
4
Views
1K
ODE with constant coefficient ##b##
  • · Replies 11 ·
Replies
11
Views
1K