Question Number 30485 by abdo imad last updated on 22/Feb/18
$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\forall\:{x}>\mathrm{0}\:\:\:\frac{{x}}{{x}+\mathrm{1}}\:\leqslant\:{ln}\left(\mathrm{1}+{x}\right)\leqslant{x} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{put}\:\:{S}_{{n}} =\:\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}\:+\:\frac{{k}}{{n}}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{S}_{{n}} \:\:. \\ $$
Commented by chantriachheang last updated on 23/Feb/18
$$\boldsymbol{{well}},\:\boldsymbol{{it}}\:\boldsymbol{{is}}\:\boldsymbol{{a}}\:\boldsymbol{{famous}}\:\boldsymbol{{problem}}\hat {\:}\wedge\wedge \\ $$