Question

[Nguyễn Đình Việt Dũng]

ai làm giúp mình với mình cần gấp

Answer 1

[Lê Song Phương]

Câu 3)

\(A=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)

\(A=\frac{3-2}{2\times3}+\frac{4-3}{3\times4}+\frac{5-4}{4\times5}+\frac{6-5}{5\times6}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}=\frac{1}{2}-\frac{1}{6}=\frac{1}{3}\)

Câu 4) 

\(B=\frac{3}{2\times5}+\frac{3}{5\times8}+\frac{3}{8\times11}+\frac{3}{11\times14}\)

\(B=\frac{5-2}{2\times5}+\frac{8-5}{5\times8}+\frac{11-8}{8\times11}+\frac{14-11}{11\times14}\)

\(B=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}=\frac{1}{2}-\frac{1}{14}=\frac{3}{7}\)

Answer 2

[Lê Song Phương]

Câu 2) 

\(B=\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{486}\)

\(\Rightarrow3\times B=3\times\left(\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}+\frac{5}{486}\right)\)

\(3\times B=\frac{15}{2}+\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}\)

\(\Rightarrow3\times B-B=\frac{15}{2}+\frac{5}{2}+\frac{5}{6}+\frac{5}{18}+\frac{5}{54}+\frac{5}{162}-\frac{5}{2}-\frac{5}{6}-\frac{5}{18}-\frac{5}{54}-\frac{5}{162}-\frac{5}{486}\)

\(\Rightarrow2\times B=\frac{15}{2}-\frac{5}{486}=\frac{3645-5}{486}=\frac{3640}{486}=\frac{1820}{243}\)

\(\Rightarrow B=\frac{1820}{243}:2=\frac{910}{243}\)