The probability of getting \(k\) heads when flipping \(n\) coins is:

\[\sum_{k=0}^{n} {n \choose k} = 2^n \]

\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]

An Identity of Ramanujan

\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} =

1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}

{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]

( ... more later !!! )

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