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Question Number 120982 by Khalmohmmad last updated on 04/Nov/20

Answered by Dwaipayan Shikari last updated on 04/Nov/20

Σ_(k=2) ^(625) log_5 (1−(1/k))  =log_5 ((1/2).(2/3).(3/4).....((624)/(625)))=−4

$$\underset{{k}=\mathrm{2}} {\overset{\mathrm{625}} {\sum}}{log}_{\mathrm{5}} \left(\mathrm{1}−\frac{\mathrm{1}}{{k}}\right) \\ $$$$={log}_{\mathrm{5}} \left(\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{2}}{\mathrm{3}}.\frac{\mathrm{3}}{\mathrm{4}}.....\frac{\mathrm{624}}{\mathrm{625}}\right)=−\mathrm{4} \\ $$

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