Solve $\sum_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)}$:
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举一反三
- Solve $\sum_{n=1}^{\infty}\frac{2n-1}{2^n}$:<br/>______
- 下面级数求和错误的是 A: $\sum_{n=0}^\infty q^n = \frac{1}{1-q} (0\lt q\lt1) $ B: $\sum_{n=1}^\infty \frac{x^{2^{n-1}}}{1-x^{2^n}} = \frac{x}{1-x} (|x|\lt 1) $ C: $\sum_{n=1}^\infty \frac{1}{{n!}} = e $ D: $\sum_{n=1}^\infty \frac{x^{2^{n-1}}}{1-x^{2^n}} = \frac{1}{1-x} (x>1) $
- 函数$f(x)=\arcsin(\sin x)$的傅里叶级数展开式为 A: $x$ B: $$\frac{4}{\pi}\sum_{n=0}^{\infty}\frac{(-1)^n\sin(2n+1)x}{(2n+1)^2}$$ C: $$\frac{4}{\pi}\sum_{n=1}^{\infty}\frac{(-1)^n\sin(2n+1)x}{(2n+1)^2}$$ D: $$\frac{4}{\pi}\sum_{n=1}^{\infty}\frac{(-1)^{n-1}\sin(2n+1)x}{(2n+1)^2}$$
- 下列级数中,收敛的是（ ）. A: \(<br/>\sum\limits_{n = 1}^\infty { { 1 \over n}} \) B: \(<br/>\sum\limits_{n = 1}^\infty { { 1 \over { { n^2}}}} \) C: \(<br/>\sum\limits_{n = 1}^\infty { { 1 \over {\sqrt n }}} \) D: \( \sum\limits_{n = 1}^\infty { { 1 \over {\root 3 \of { { n^2}} }}} \)
- Solve $ \lim_{n \rightarrow +\infty}\int_0^1 \frac{dx}{1+x^n}=$ :<br/>______