Question Number 120982 by Khalmohmmad last updated on 04/Nov/20
Answered by Dwaipayan Shikari last updated on 04/Nov/20
$$\underset{{k}=\mathrm{2}} {\overset{\mathrm{625}} {\sum}}{log}_{\mathrm{5}} \left(\mathrm{1}−\frac{\mathrm{1}}{{k}}\right) \\ $$$$={log}_{\mathrm{5}} \left(\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{2}}{\mathrm{3}}.\frac{\mathrm{3}}{\mathrm{4}}…..\frac{\mathrm{624}}{\mathrm{625}}\right)=−\mathrm{4} \\ $$