Question Number 122859 by mnjuly1970 last updated on 20/Nov/20
$$\:\:\:\:\:\:\:\:\:\:\:\:...\:{calculus}\left({II}\right)−\:\:{analysis}\left({I}\right)... \\ $$$$\:\:\::::\:\:{consider}\:{the}\:{sequence}\:\left\{{c}_{{n}} \right\}_{{n}=\mathrm{1}} ^{\infty} \\ $$$$\:\:{in}\:{which}\:::\:{c}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+...+\frac{\mathrm{1}}{{n}}\:−{ln}\left({n}\right) \\ $$$$\:\:\:{prove}\:{that}\:{the}\:{above}\:{sequence}\:{is} \\ $$$$\:\:\:{convergent}\:\:{and}\:{then}\: \\ $$$$\:\:\:{find}\:{its}\:{limit}. \\ $$