Question

Arătați ca
[1+1/2]×[1+1/3]=2

Calculați
{1+1/2]×[1+1/3×...×[1+1/45]

Answer 1

[tex](1+\frac{1}{2})(1+\frac{1}{3})=\frac{3}{2}\cdot\frac{4}{3}=2\\ (1+\frac{1}{n})(1+\frac{1}{n+1})=\frac{n+1}{n}\cdot\frac{n+2}{n+1}=\frac{n+2}{n}\\ \frac{4}{2}\cdot\frac{6}{4}\cdot\frac{8}{6}...\frac{44}{42}\cdot\frac{46}{44}=\frac{46}{2}=23 [/tex]