Question

Чему равно произведение (1+1/2)(1+1/3)…(1+1/2015)?

Answer 1

$(1+\frac{1}{2})(1+\frac{1}{3})(1+\frac{1}{4})\cdot ...\cdot (1+\frac{1}{2013})(1+\frac{1}{2014})(1+\frac{1}{2015})=\\\\=\frac{3}{2}\cdot \frac{4}{3}\cdot \frac{5}{4}\cdot ...\cdot \frac{2014}{2013}\cdot \frac{2015}{2014}\cdot \frac{2016}{2015}=\frac{2016}{2}=1008$