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Question Number 55905 by gunawan last updated on 06/Mar/19

$$\underset{n\to \mathrm{\infty }}{\lim }(x_{2n}+x_{2n+1})=315$$$$\underset{n\to \mathrm{\infty }}{\lim }(x_{2n}+x_{2n-1})=2016$$$$\underset{n\to \mathrm{\infty }}{\lim }\frac{x_{2n}}{x_{2n+1}}=...$$

Answered by tanmay.chaudhury50@gmail.com last updated on 06/Mar/19

$$\underset{n\to \mathrm{\infty }}{\lim }(x_{2n}+x_{2n+1})⩾\underset{n\to \mathrm{\infty }}{\lim }2\left(\sqrt{x_{2n}\times x_{2n+1}}\right)$$$$\underset{n\to \mathrm{\infty }}{\lim }(x_{2n}+x_{2n-1})⩾\underset{n\to \mathrm{\infty }}{\lim 2}\left(\sqrt{x_{2n}\times x_{2n-1}}\right)$$$$\frac{\underset{n\to \mathrm{\infty }}{\lim }\left(\sqrt{x_{2n}\times x_{2n+1}}\right)}{\underset{n\to \mathrm{\infty }}{\lim }\left(\sqrt{x_{2n}\times x_{2n-1}}\right)}⩽\frac{315}{2016}$$$$$$$$wait....$$

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