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Question Number 127455 by snipers237 last updated on 29/Dec/20

P r o v e t h a t f o r a l l n ⩾ 1

1) T h e r e e x i s t a_{n} \in] 0, 1 [s u c h a s

s i n (\frac{1}{n}) = \frac{1}{n} - \frac{1}{6 n^{3}} c o s (\frac{1}{n} a_{n})

2) P r o v e t h a t \lim_{n \to \infty} a_{n} = \frac{1}{10}