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Combining power series Use the geometric
Chapter 8, Problem 26E(choose chapter or problem)
QUESTION:
Combining power series Use the geometric series
\(f(x)=\frac{1}{1-x}=\sum_{k=0}^{\infty} x^{k}\), for |x| < 1,
to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.
\(f(-4 x)=\frac{1}{1+4 x}\)
Questions & Answers
QUESTION:
Combining power series Use the geometric series
\(f(x)=\frac{1}{1-x}=\sum_{k=0}^{\infty} x^{k}\), for |x| < 1,
to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.
\(f(-4 x)=\frac{1}{1+4 x}\)
ANSWER:Solution 26EStep 1:Given thatUse the geometric series Step2:To find The power series repre