# Questions tagged [summation]

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### Does $\sum\limits_{k=2}^{\infty}{\frac{|B_{k}|}{k!}(\cos(n)-1)}$ have a closed form?

I am trying to find a closed form expression of the following sum in terms of $n$ (if it exists) where $B_{k}$ is the $k$th Bernoulli number. $$\sum_{k=2}^{\infty}{\frac{|{B_{k}|}}{k!}(\cos(n)-1)}$$ ...
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### Sum manipulation

my question is if these two sums are equal: $\sum_{j=1}^n \lambda u_jx_j + \mu v_j x_j = \sum_{j=1}^n \lambda u_jx_j + \sum_{j=1}^n \mu v_jx_j$ Thank you for your help.
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### How to evaluate/calculate sums? [closed]

If you have this expression, $$x + x/2 + x/4 + x/8 + \ldots$$, it equates to roughly $2x$, why is this? Which area of maths is this? To deal with these kind of sums, and getting a result. I am ...
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### why this statement about $\sum_{i=0}^n a_n$ is false?

Given that ${a_n}$ is positive series, and $\sum_{i=0}^n a_n$ is converge: -There is a sub-series for ${a_n}$ that converge to S>$0$. (THIS statement is false) why is this statement false?