\[\large \displaystyle\sum_{n=1}^{\infty} \dfrac{f(n)}{n} \]

Let \(S\) denote the expression of the variable sum above where \(f(n)\) has a 50% chance of being 1 and a 50% chance of being -1 for each individual \(n\), (with the \(f(n)\)'s being independent of one another).

What is the probability that the series \(S\) converges?

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