Question

Hei! Am nevoie de ajutor la problema 1)

Answer 1

Folosim relatia:$\frac{1}{n-2}-\frac{1}{n}=\frac{2}{(n-2)n}$

Atunci relatia initiala devine:

$\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7} +...\frac{1}{n-2}-\frac{1}{n}=\frac{332}{999}$

Dupa reducerea termenilor asemenea se obtine:

$\frac{1}{3}-\frac{1}{n}=\frac{332}{999}$

Aducem la acelasi numitor in membrul stang:

$\frac{n-3}{3n} =\frac{332}{999}$⇒999(n-3)=332*3n⇒999n-2997=996n⇒999n-996n=2997⇒3n=2997⇒n=999