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1+1solve this |
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Answer» Let y = 1 + \(\frac{1}{1+\frac{1}{1+....}}\) y = 1 + \(\frac{1}{y}\) (because infinite terms having no problem) y - 1 = \(\frac{1}{y}\) \(\Rightarrow\) y2 - y - 1 = 0 \(\Rightarrow\) y = \(\frac{1\pm\sqrt{1+4}}{2}\) y = \(\frac{1\pm\sqrt{5}}{2}\) Since, y = \(\frac{1\pm\sqrt{5}}{2}\) = -ve,(not possible) but clearly y is sum of positive terms. therefore, y = \(\frac{1+\sqrt5}{2}\) So, option B is correct. |
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