→ yhliu :|1-sin(1/n)/(1/n)|≦(1/n^2)/3! 交錯級數誤差定理. 04/13 23:15
sin(1/n) (1/n)^2 (1/n)^4
1- ───── = - ──── + ──── - ... =: a_n
1/n 3! 5!
(1/n)^2 (1/n)^4 (1/n)^2 (1/n)^2
│a_n│ <= ──── + ──── + ... <= ──── + ──── + ...
3! 5! 3! 5!
= (1/n)^2 * (1/3! + 1/5! + ...)
~~~~~~~~~~~~~~~~~~~
└→ (e-(1/e)-2)/2
By comparison test, summation a_n converges absolutely
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