Question

Ma puteri ajuta cu problema :
Va rog !! Dau 50 puncte

Answer 1

Răspuns:

Explicație pas cu pas:

$=2*(\frac{3}{2*5}+\frac{3}{5*8} +...+\frac{3}{284*287} )=2*(\frac{1}{2}-\frac{1}{5}+\frac{1}{5} -\frac{1}{8}+...+\frac{1}{284}-\frac{1}{287})=2*(\frac{1}{2}-\frac{1}{287})=2*\frac{285}{287} =\frac{570}{287}.$

Answer 2

$\frac{6}{2 \times 5} + \frac{6}{5 \times 8} + \frac{6}{8 \times 11} + ... + \frac{6}{284 \times 287} =$

$= \frac{2 \times 3}{2 \times 5} + \frac{2 \times 3}{5 \times 8} + \frac{2 \times 3}{8 \times 11} + ... + \frac{2 \times 3}{284 \times 287} =$

$= 2 \times (\frac{3}{2 \times 5} + \frac{3}{5 \times 8} + ... + \frac{3}{284 \times 287} ) =$

$= 2 \times \frac{285}{2 \times 287} =$

$= \frac{285}{287}$

$\frac{3}{2 \times 5} + \frac{3}{5 \times 8} + ... + \frac{3}{284 \times 287} =$

$= \frac{5 - 2}{2 \times 5} + \frac{8 - 5}{5 \times 8} + ... + \frac{287 - 284}{284 \times 287} =$

$= \frac{5}{2 \times 5} - \frac{2}{2 \times 5} + \frac{8}{5 \times 8} - \frac{5}{5 \times 8} + ... +$

$\frac{287}{284 \times 287} - \frac{284}{284 \times 287} =$

$= \frac{1}{2} - \frac{1}{5} + \frac{1}{5} - ... + \frac{1}{284} - \frac{1}{287} =$

$= \frac{1}{2} - \frac{1}{287} =$

$= \frac{287}{2 \times 287} - \frac{2}{2 \times 287} =$

$= \frac{287 - 2}{2 \times 287} =$

$= \frac{285}{2 \times 287}$

Sper că te-am ajutat. Succes!