Răspuns:
Explicație pas cu pas:
daca grupa primul cu ultimul, urmatorul cu penultimul si tot asa obtinem
[tex]\frac{1}{1521} +\frac{1}{2020} +\frac{1}{1522}+\frac{1}{2019} +...[/tex]
avem 500 termeni deci 250 de grupe
fiecare grupa va fi astfel
[tex]\frac{1}{1521} +\frac{1}{2020} \geq \frac{4}{3541} \\\\\frac{1}{1522}+\frac{1}{2019} \geq \frac{4}{3541}\\....[/tex]
deci daca adunam vom avea
[tex]\frac{1}{1521} +\frac{1}{2020} +\frac{1}{1522}+\frac{1}{2019} +...\geq 250 \cdot \frac{4}{3541}\\\\\frac{1}{1521} +\frac{1}{2020} +\frac{1}{1522}+\frac{1}{2019} +...\geq \frac{1000}{3541}[/tex]
[tex]\frac{1000}{3541} =0,28>\frac{1}{4}[/tex]
Deci
[tex]\frac{1}{1521} +\frac{1}{2020} +\frac{1}{1522}+\frac{1}{2019} +...>\frac{1}{4}[/tex]
