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Question Number 55640 by gunawan last updated on 01/Mar/19

$$\mathrm{known}\mathrm{real}\mathrm{numbers}\mathrm{sequence}$$$$\left\{a_n\right\}\mathrm{and}\left\{b_n\right\}\mathrm{both}\mathrm{of}\mathrm{them}$$$$\mathrm{convergences}\mathrm{to}0.$$$$\mathrm{If}\left\{b_n\right\}\mathrm{monotonous}\mathrm{descend}$$$$\mathrm{and}\underset{n\to \mathrm{\infty }}{\lim }\frac{a_{n+1}-a_n}{b_{n+1}-b_n}.$$$$\mathrm{then}\underset{n\to \mathrm{\infty }}{\lim }\frac{a_n}{2b_n}=..$$

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