Using calculus, prove (for ) that is monotone (increasing) and bounded above. Find its limit.

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- Jan 15th 2012, 03:21 PMalexmahoneProve that the sequence is monotone and bounded above
Using calculus, prove (for ) that is monotone (increasing) and bounded above. Find its limit.

- Jan 16th 2012, 04:10 AMemakarovRe: Prove that the sequence is monotone and bounded above
Expand sin(x) as x + O(x); then the limit of becomes obvious. To prove monotonicity and boundedness, expand as . This series satisfies the conditions to the alternating series test. From the info on that page, . Also, . You can show that , so .

Another way to show monotonicity is to consider and show that its derivative is eventually positive (also using series). - Jan 16th 2012, 06:11 AMchisigmaRe: Prove that the sequence is monotone and bounded above
Setting You have...

Kind regards