Solution Found!
Power series from the geometric series Use the
Chapter 1, Problem 25RE(choose chapter or problem)
QUESTION:
Use the geometric series \(\sum _{k=0}^{\infty}\ x^k=\frac{1}{1-x}\), for |x| < 1 to determine the Maclaurin series and the interval of convergence for the following functions.
\(f(x)=\frac{1}{(1-x)^2}\)
Questions & Answers
QUESTION:
Use the geometric series \(\sum _{k=0}^{\infty}\ x^k=\frac{1}{1-x}\), for |x| < 1 to determine the Maclaurin series and the interval of convergence for the following functions.
\(f(x)=\frac{1}{(1-x)^2}\)
ANSWER:Solution 25RE
Step 1:
In this problem we have to use the geometric series for |x|<1, to determine the Maclaurin series of and also we have to find the interval of convergence
We have