Consider a function $f(k)$ defined for positive integers $k=1,2,\cdots \infty$ the function is satisfies the condition $f(1)+f(2)+\cdots = p/(p-1)$, where $0
Consider a function $f(k)$ defined for positive integers $k=1,2,\cdots \infty$ the function is satisfies the condition $f(1)+f(2)+\cdots = p/(p-1)$, where $0
$$ \sum_{n=1}^\infty f(n) = - \sum_{n=1}^\infty p^n = -\frac{p}{1-p} = \frac{p}{p-1}$$
– 2011-11-12