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Calculati: [tex][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}) [/tex]

Răspuns :

[tex]...=(1-\dfrac12+1-\dfrac23+1-\dfrac34+...+1-\dfrac{999}{1000}):[/tex]

[tex]:(\dfrac12+\dfrac13+\dfrac14+...+\dfrac{1}{1000})=[/tex]

[tex]=(\dfrac12+\dfrac13+\dfrac14+...+\dfrac{1}{1000}):(\dfrac12+\dfrac13+\dfrac14+...+\dfrac{1}{1000})=1[/tex]