Question

Calculati: $[999-( \frac{1}{2} + \frac{2}{3} + \frac{3}{4} +...+ \frac{999}{1000} )]:( \frac{1}{2} + \frac{1}{3} + \frac{1}{4} +...+ \frac{1}{1000})$

Answer 1

$...=(1-\dfrac12+1-\dfrac23+1-\dfrac34+...+1-\dfrac{999}{1000}):$

$:(\dfrac12+\dfrac13+\dfrac14+...+\dfrac{1}{1000})=$

$=(\dfrac12+\dfrac13+\dfrac14+...+\dfrac{1}{1000}):(\dfrac12+\dfrac13+\dfrac14+...+\dfrac{1}{1000})=1$