The value of $$0$$·$$2log5$$⁡$$14+18+116+$$⋯ is

Question

The value of $$0$$·$$2log5$$⁡$$14+18+116+$$⋯ is

Infinity Learn · Accepted Answer

We have,$$14+18+116+$$⋯$$=1/41$$−$$1/2=12Hence$$,$$0.2log5$$⁡ $$14+18+116+$$⋯$$=0.2log5$$⁡ $$12$$                                           $$=15log5$$⁡$$12$$                                          $$=5$$−$$12log$$⁡$$512$$                                         $$=(5)$$−$$2log5$$⁡$$12$$                                         $$=(5)log5$$⁡$$4$$                                         $$=4$$

The value of ${(0 \cdot 2)}^{\log_{\sqrt{5}} (\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots)}$ is

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The value of 0·2log5⁡14+18+116+⋯ is

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The value of ${(0 \cdot 2)}^{\log_{\sqrt{5}} (\frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots)}$ is