Ta có : C = \(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{2013}\right)=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{2014}{2013}=\frac{3.4.5...2014}{2.3.4...2013}=\frac{2014}{2}=1007\)
\(C=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).....\left(1+\frac{1}{2013}\right)\)
\(C=\frac{3}{2}.\frac{4}{3}.....\frac{2014}{2013}\)
\(C=\frac{2014}{2}=1007\)
\(C=\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{4}\right)\times.....\times\left(1+\frac{1}{2013}\right)\)
\(C=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times....\times\frac{2014}{2013}\)
\(C=\frac{3\times4\times5\times.....\times2014}{2\times3\times4\times.....\times2013}\)
\(C=\frac{2014}{2}\)
\(C=1007\)
