Question

Exercitiul 7 rezolvarea completa va rog! Dau coroana

Answer 1

[tex]\frac{5}{n(n+5)}=\frac{n+5-n}{n(n+5)}=\frac{1}{n}-\frac{1}{n+5}\\ Aplicam\ si\ in\ acest\ exercitiu:\\ A=\frac{1}{1\cdot6}+\frac{5}{6\cdot 11}+\frac{5}{11\cdot 16}+....+\frac{5}{201\cdot 206}\\ \\ A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+......+\frac{1}{201}-\frac{1}{206}\\ \\ A=1-\frac{1}{206}\\ \\ \boxed{A=\frac{205}{206}}[/tex]