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Question Number 40893 by abdo.msup.com last updated on 28/Jul/18

l e t u_{k} = 1 - {(1 - \frac{1}{2^{k}})}^{n - 1}

1) p r o v e t h a t Σ u_{k} c o n v e r g e s

2) l e t f (x) = 1 - {(1 - \frac{1}{2^{x}})}^{n - 1} w i t h x ⩾ 0

p r o v e t h a t \forall p \in N

\sum_{k = 1}^{p + 1} u_{k} ⩽ \int_{0}^{p + 1} f (x) d x ⩽ \sum_{k = 0}^{p} u_{k}