Question

VA ROOOG! AM NEVOIE DE REZOLVAREA PROBLEMEI!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

daca grupa primul cu ultimul, urmatorul cu penultimul si tot asa  obtinem

$\frac{1}{1521} +\frac{1}{2020} +\frac{1}{1522}+\frac{1}{2019} +...$

avem 500 termeni deci 250 de grupe

fiecare grupa va fi astfel

$\frac{1}{1521} +\frac{1}{2020} \geq \frac{4}{3541} \\\\\frac{1}{1522}+\frac{1}{2019} \geq \frac{4}{3541}\\....$

deci daca adunam vom avea

$\frac{1}{1521} +\frac{1}{2020} +\frac{1}{1522}+\frac{1}{2019} +...\geq 250 \cdot \frac{4}{3541}\\\\\frac{1}{1521} +\frac{1}{2020} +\frac{1}{1522}+\frac{1}{2019} +...\geq \frac{1000}{3541}$

$\frac{1000}{3541} =0,28>\frac{1}{4}$

Deci

$\frac{1}{1521} +\frac{1}{2020} +\frac{1}{1522}+\frac{1}{2019} +...>\frac{1}{4}$