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Results tagged with sequences-and-series
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user 519749
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
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Finding the smallest possible value of $|S_n|$ for Sequence and Series in real analysis [closed]
Let $𝑋_1,𝑋_2, … , 𝑋_𝑛$ be a sequence of independent random variables with $𝑃(𝑋_𝑛 = 4^𝑛) =
𝑃(𝑋_𝑛 = −4^𝑛) = \frac12$. Let $𝑆_𝑛 = 𝑋_1 + 𝑋_2 + ⋯ + 𝑋_𝑛$. If $A_n=\sup\, \{𝑟 ∈ \Bbb R: 𝑃( …
