If I know that $a_{n}=f(n)$, is there any reliable means of finding a non-recursive equation for the partial sum from 1 to some n?
Find the formula for the partial sum of a series from its corresponding sequence
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calculus
sequences-and-series
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3In general, no. Do you have a specific series in mind? – 2012-02-29
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0The answer is no since your function is $C^\infty$ howerever if you function is a Polinomial the series will be divergent. – 2012-02-29
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0There is no general method. There are methods for certain restriced classes of functions $f(n)$, such as polynomials. – 2012-03-01