Prove that if $$x_n>0, \forall n \in N$$ is such that $$lim \frac{x_{n+1}}{x_n}=a<1$$ then $$lim x_n=0 $$ I feel absolutely frustrated, because I tried a lot on this issue and couldn't develop anything. Does anyone have anything that can help me?
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$\begingroup$ math.stackexchange.com/q/2508842/42969, math.stackexchange.com/q/714558/42969, math.stackexchange.com/q/1242096/42969 $\endgroup$– Martin RNov 20 at 20:29
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$\begingroup$ $~0 < a < 1 \implies \displaystyle \lim_{n \to \infty} a^n = 0.$ $\endgroup$– user2661923Nov 20 at 20:33
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$\begingroup$ I managed to solve it! $\endgroup$– Gabrielle SantosNov 20 at 20:43
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