I need to compute $$f(x)=\sum_{i=0}^\infty \left(\left\lfloor\frac{i}{2^x}\right\rfloor+x+1\right)(1-p)^{i-1}p$$and minimize it with respect to $x$ (an expression which will depend on $p$).
Compute infinite sum
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sequences-and-series
functional-analysis
discrete-mathematics
, so $\sum_i(x+1)(1-p)^{i-1}p$ is finite for all $x$.
– 2012-12-29