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2
questions
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Evaluate the following series sum.
Problem
I’m trying to evaluate the following series sum
\begin{equation}
S_{j}(z) = \sum_{k=1}^{\infty} \frac{2 H_{k} z^{k+2}}{(k+1)(k+2)^{j}}
\end{equation}
Where
\begin{equation}
H_{k} = \sum_{n=1}^{...
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2
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How can I prove that the following function is increasing in $x \in [0,1]$?
How can I prove that the following function is increasing in $x$: $$\sum_{i=1}^{\infty} x (1-x) ^ {i-1} \log \left (1+ \mu (1-x)^{i-1} \right)$$
where $\mu$ is any non-negative number and $x$ is in $[...
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