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What is the sum of the series $1+ln2+(((ln2)^2)/(2!))+...+(((ln2)^n)/(n!))+...$ ?

1 Answer

May 10, 2018

2

Explanation:

By definition of the exponential function:

$e^Omega = sum_(k = 0)^oo Omega^k/(k!) = 1 + Omega + (Omega^2)/(2!) + ... + (Omega^n)/(n!) + ...$

Look at the pattern:

$Omega = ln 2$

And so you are evaluating:

$color(red)(e^(ln(2)) = 2)$

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