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nick's question at Yahoo! Answers (Maclaurin series)

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661
Hello nick,

If $|t|<1$ we know that $\dfrac{1}{1-t}=\displaystyle\sum_{n=0}^{\infty}t^n$. Then, using the Algebra of series: $$f(x)=x\cdot\dfrac{1}{1-x^4}=x\sum_{n=0}^{\infty}(x^4)^n=\sum_{n=0}^{ \infty}x^{4n+1}\quad (|x|<1)$$ So, necessarily the Maclaurin series for $f(x)$ is $\displaystyle\sum_{n=0}^{\infty}x^{4n+1}.$