# Tagged Questions

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### Is $f(x)=\sum_{k\in\mathbb N}\frac1k\sin\frac x{2^k}$ bounded?

$$f(x)=\sum_{k\in\mathbb N}\frac1k\sin\frac x{2^k}$$Is this function bounded? So obviously this converges because $|\frac1k\sin\frac x{2^k}|<|\frac x{2^k}|$ and $\sum\frac x{2^k}$ converges by ...
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### Evaluating $\lim_{n\to\infty} \left({1\over1\cdot2\cdot3}+{1\over2\cdot3\cdot4}+\cdots+{1\over(n-1)\cdot n\cdot(n+1)}\right)$

The original question was to find $L=\displaystyle\lim_{n\to\infty}\sum_{k=1}^na_k$ where $a_n=\displaystyle{n\over(1+2+\cdots+(n-1))(1+2+\cdots+n)}$, which I managed to get down to evaluating the ...
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### Prove that if $\sum_{n=1}^\infty a_{n}$ is absolutely convergent, then $|\sum_{n=1}^\infty a_{n}| \leq | \sum_{n=1}^\infty |a_{n}|$

Hey everyone this was given as a practice problem for my first year calculus class and it really giving me a headache, any help is appreciated! Prove that if $\sum_{n=1}^\infty a_{n}$ is absoultley ...
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### How to solve this summation (Lerch Transcendent)?

How is it possible to deduce the closed form of the following? $$\sum_{i = 0}^{n - 1} \frac{2^i}{n - i} = ?$$