Hello!(adsbygoogle = window.adsbygoogle || []).push({});

Please help me to solve following exercise (2.5.8) from Elementary Real Analysis by Thomson-Bruckner:

Suppose that a sequence [itex]\{s_n\}[/itex] of positive numbers satisfies the condition [itex] s_{n+1} > \alpha s_n [/itex] for all ##n## where ##\alpha>1.## Show that ##s_n \to \infty.##

I can't prove this using definition and given condition, I can only give an example of such sequence, ##\exp n## with ##\alpha = 2## but it seems useless for me. The only I know is that sequence is monotone and unbounded and so diverges.

I'm only asking about a little hint that will give me a possibility to solve this by myself.

Thanks a lot.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proving divergence of a sequence

**Physics Forums | Science Articles, Homework Help, Discussion**