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Determine a power series representation for the function g(x)=ln(7−x).

Determine a power series representation for the function g(x)=ln(7−x). Correct Answer ln(7)∞∑n=0 xn+1/7n+1

We know that ∫1/7−x dx=−ln(7−x) and there is a power series representation for 1/7−x. So, ln(7−x)=−∫1/7−xdx =−∫ ∞∑n=0 xn/7n+1dx=C ⇒ ∞∑n=0 xn+1/7n+1 So, the answer is, ln(7−x)=ln(7)∞∑n=0 xn+1/7n+1.

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