This document discusses the convergence of sequences and series, analyzing their limits and behavior.
Contents
Convergence of the sequence Sn n1
Divergence of the sequence Vn n1
Convergence of the sequence un 1 and limit values of the sequences un 1 and Sn n1
Convergence of the sequence Sn n1
Divergence of the sequence Vn n1
Convergence of the sequence un 1 and limit values of the sequences un 1 and Sn n1
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Extract
[...] The limit S is therefore in Divergence of the sequence n>1. For all : Or : Donc : Thus : On Thus the general term sequence diverge to 1 and n?1. According to question we have: Now the limit of in est , name fini. Thus ) converge towards The suite is strictly positive, increasing, and converges to . [...]
[...] Study of two series of sums Convergence of the sequence n?1. For all , on a : So, for all : Thus, the continuation is strictly increasing. On calculates first from : Or : et : Donc : So : Donc : Finally : According to question we have: The central terms cancel each other out and therefore there is therefore: Or . From where: According to question the continuation is growing. As is positive for all not null, according to the question , is dominated by . [...]
