Let be the series....[tex] S=\sum_{n=0}^{\infty} a(n) [/tex](adsbygoogle = window.adsbygoogle || []).push({});

where a(0)=1=a(1) and the rest of coefficients satisfy a recurrence relation (linear or non-linear) so [tex] F(n,a_{n+2} , a_{n+1},a_{n})=n [/tex] :tongue2: :tongue2: ..then my question is let's suppose that the series has an "optimum number of terms" K so if you take k-terms the series converges to a optimum value, otherwise the series (taking all terms) diverges) my question is how would we obtain this k and the sum of the series... a "brute force" algorithm would say that you take a big number of terms and solve the recurrence by using a computer...

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# Sum of a series

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