題組內容
| 6. Consider the series: $$\sum_{n=0}^{\infty} \frac{x^n}{(n+1)(n+2)}$$
(b) (6 points) Show that for $|x| < 1$:
$$\sum_{n=0}^{\infty} \frac{x^n}{(n+1)(n+2)} = \frac{1 - x}{x^2} \ln(1 - x) + \frac{1}{x}$$
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| 6. Consider the series: $$\sum_{n=0}^{\infty} \frac{x^n}{(n+1)(n+2)}$$
(b) (6 points) Show that for $|x| < 1$:
$$\sum_{n=0}^{\infty} \frac{x^n}{(n+1)(n+2)} = \frac{1 - x}{x^2} \ln(1 - x) + \frac{1}{x}$$