- #1
annoymage
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Homework Statement
Results
i) if [itex](a_n)[/itex] tends to L as n tends to infinity, then [itex]a_{n_r}[/itex] tends to L as r tend to infinity
ii)if [itex](a_n)[/itex] tends to infinity as n tends to infinity, then [itex]a_{n_r}[/itex] tends to infinity as r tend to infinity
using this result prove that
if [itex](a_n)[/itex] is an increasing sequence, prove that the converse of i) is true
Suppose [itex](a_n)[/itex] is divergent, then by ii), all the subsequences must be divergent, so, cant.
therefore [itex](a_n)[/itex] must be convergent, means [itex](a_n)[/itex] tends to M for some M,
apply i), then means M=L
but how come i didn't use the fact [itex](a_n)[/itex] is monotone, must be something wrong somewhere, help T_T