- Stolz-Cesàro theorem
In
mathematics , the Stolz-Cesàro theorem is a criterion for proving the convergence of asequence .Let a_n)_{n geq 1} and b_n)_{n geq 1} be two
sequence s ofreal number s. Assume that b_n is positive, strictly increasing andunbounded and the following limit exists::lim_{n o infty} frac{a_{n+1}-a_n}{b_{n+1}-b_n}=l.
Then, the limit:
:lim_{n o infty} frac{a_n}{b_n}
also exists and it is equal to l.
The Stolz-Cesàro theorem can be viewed as a generalization of the
Cesàro mean , but also as a l'Hôpital's rule for sequences.The theorem is named after
mathematician sOtto Stolz andErnesto Cesàro .----
External links
* [http://planetmath.org/encyclopedia/ProofOfStolzCesaroTheorem.html Proof of Stolz-Cesàro theorem]
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