# No harmonic, no foul

Calculus Level 4

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

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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