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## Main Question or Discussion Point

Hello!

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.

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.