- #1
dimanet
- 3
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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.