Question

Exercitiul 24 va rog

Answer 1

[tex]a)x=\sqrt{\frac{12}{11}+\frac{13}{22}+\frac{14}{33}+..+\frac{110}{1089}-(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{99})}\\ x=\sqrt{(\frac{12}{11}-1)+(\frac{13}{22}-\frac{1}{2})+...+(\frac{110}{1089}-\frac{1}{99})}\\ x=\sqrt{\frac{1}{11}+\frac{2}{22}+\frac{3}{33}+...+\frac{99}{1089}}\\ x=\sqrt{\underbrace{\frac{1}{11}+\frac{1}{11}+...+\frac{1}{11}}}\\ ~~~~~~~~~~~~~~~~de\ 99\ ori\\ x=\sqrt{\frac{99}{11}}\Rightarrow\bold{x=3}\\ \\ [/tex]
[tex]b)x=\sqrt{\frac{8}{7}+\frac{9}{14}+\frac{10}{21}+...+\frac{350}{2401}-(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{343})}\\ x=\sqrt{(\frac{8}{7}-1)+(\frac{9}{14}-\frac{1}{2})+.....+(\frac{350}{2401}-\frac{1}{343})}\\ x=\sqrt{\frac{1}{7}+\frac{2}{14}+....+\frac{343}{2401}}\\ x=\sqrt{\underbrace{\frac{1}{7}+\frac{1}{7}+...+\frac{1}{7}}}\\ ~~~~~~~~~~~~de\ 343\ ori\\ x=\sqrt{\frac{343}{7}}\Rightarrow \bold{x=7}[/tex]