Question

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

(a) ∞∑n=0 x^n+1/7^n+1

(b) ln(14)∞∑n=0 x^n+1/7n

(c) ln(7)∞∑n=0 x^n+1/7^n+1

(d) ln∞∑n=0 x/7^n+1

I have been asked this question in an interview.

I'm obligated to ask this question of Discrete Probability topic in section Discrete Probability of Discrete Mathematics

Answer 1

The correct choice is (c) ln(7)∞∑n=0 x^n+1/7^n+1

The best explanation: 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 x^n/7^n+1dx=C

    ⇒ ∞∑n=0 x^n+1/7^n+1

So, the answer is, ln(7−x)=ln(7)∞∑n=0 x^n+1/7^n+1.