Let ∑ n = 0 ∞ c n x n {\displaystyle \sum _{n=0}^{\infty }c_{n}x^{n}} be the Maclaurin series for f ( x ) = 4 1 + 2 x + 1 1 + x {\displaystyle f(x)={\frac {4}{1+2x}}+{\frac {1}{1+x}}} , i.e., ∑ n = 0 ∞ c n x n = 4 1 + 2 x + 1 1 + x {\displaystyle \sum _{n=0}^{\infty }c_{n}x^{n}={\frac {4}{1+2x}}+{\frac {1}{1+x}}} . Find c n {\displaystyle c_{n}} for all n {\displaystyle n} .
