Prove that for all n≥1 1)There exist a_n ∈]0,1[ such as sin((1/n))=(1/n)−(1/(6n^3 ))cos((1/n)a_n ) 2) Prove that lim_(n→∞) a


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

$P r o v e t h a t f o r a l l n ⩾ 1$ $1) T h e r e e x i s t a_{n} \in] 0, 1 [s u c h a s$ $s i n (\frac{1}{n}) = \frac{1}{n} - \frac{1}{6 n^{3}} c o s (\frac{1}{n} a_{n})$ $2) P r o v e t h a t \lim_{n \to \infty} a_{n} = \frac{1}{10}$
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