- #1
Felafel
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Homework Statement
let ##a_n## be ##a_{n+1}=\frac{1}{4-3a_n} \quad n≥1##
for which values of ##a_1## does the sequence converge? which is the limit?
The Attempt at a Solution
##0<a_1<\frac{4}{3}## because if ##a_1>\frac{4}{3}→a_2<0## not possible.
Now let's assume ##a_n## converges to M.
I have:
##M=\frac{1}{4-3M}##
##3M^2-4M+1=0 → M_{1,2}= 1, \frac{1}{3}##
However the can't be two limits, but both could work. How do I decide which one's wrong?