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 , how to determine f(k) from this information?
Find $f(k)$ form the given data
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algebra-precalculus
: $$ \sum_{n=1}^\infty f(n) = - \sum_{n=1}^\infty p^n = -\frac{p}{1-p} = \frac{p}{p-1}$$
– 2011-11-12