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Gauss's Test

If $u_n > 0$ and given $B(n)$ a bounded function of $n$ as $n\to \infty$, express the ratio of successive terms as

\begin{displaymath}
\left\vert{u_n\over u_{n+1}}\right\vert = 1 + {h\over n} + {B(n)\over n^r}
\end{displaymath}

for $r>1$. The Series converges for $h>1$ and diverges for $h\leq 1$.

See also Convergence Tests


References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 287-288, 1985.




© 1996-9 Eric W. Weisstein
1999-05-25