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- #1
DreamWeaver
Well-known member
- Sep 16, 2013
- 337
Here's an interesting limit I found the other day...
\(\displaystyle \text{limit}_{\, \epsilon \to 0^{+}}\sqrt{\epsilon + \sqrt{\epsilon + \sqrt{ \epsilon + \sqrt{\epsilon + \cdots} } } } = 1\)
It's both obvious and yet elusive... Any ideas on how to prove it...???
\(\displaystyle \text{limit}_{\, \epsilon \to 0^{+}}\sqrt{\epsilon + \sqrt{\epsilon + \sqrt{ \epsilon + \sqrt{\epsilon + \cdots} } } } = 1\)
It's both obvious and yet elusive... Any ideas on how to prove it...???