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\(\frac{1}{3}+\frac{13}{15}+\frac{33}{35}+\frac{61}{63}+\frac{97}{99}+\frac{141}{143}\)
\(=\left(1-\frac{2}{3}\right)+\left(1-\frac{2}{15}\right)+\left(1-\frac{2}{35}\right)+\left(1-\frac{2}{63}\right)+\left(1-\frac{2}{99}\right)+\left(1-\frac{2}{143}\right)\)
\(=\left(1+1+1+1+1+1\right)-\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)
\(=6-\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=6-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=6-\left(1-\frac{1}{13}\right)\)
\(=6-\frac{12}{13}\)
\(=\frac{66}{13}\)
Ủng hộ mk nha ^_-
Ta có :
Đặt \(A=\frac{31}{3}+\frac{31}{15}+...+\frac{31}{143}\)
\(A=\frac{31}{1.3}+\frac{31}{3.5}+...+\frac{31}{11.13}\)
\(\frac{2}{31}A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)
\(\frac{2}{31}A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)
\(\frac{2}{31}A=1-\frac{1}{13}\)
\(A=\frac{12}{13}:\frac{2}{31}\)
\(A=\frac{186}{13}\)
\(\Rightarrow x-\frac{186}{13}=\frac{9}{13}\)
\(x=\frac{9}{13}+\frac{186}{13}\)
\(x=\frac{195}{13}=15\)
Ủng hộ mk nha !!! ^_^
\(\text{Đặt }A=\frac{31}{3}+\frac{31}{15}+...+\frac{31}{143}\)
\(\Rightarrow A=\frac{31}{1.3}+\frac{31}{3.5}+...+\frac{31}{11.13}\)
\(\Rightarrow\frac{2}{31}A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{11.13}\)
\(\Rightarrow\frac{2}{31}A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\)
\(\Rightarrow\frac{2}{31}A=1-\frac{1}{13}\Rightarrow A=\frac{12}{13}:\frac{2}{31}=\frac{186}{13}\)
\(\Rightarrow x-\frac{186}{13}=\frac{9}{13}\)
\(\Rightarrow x=\frac{9}{13}+\frac{186}{13}\)
\(\Rightarrow x=\frac{195}{13}=15\)
\(\frac{1}{3}+\frac{13}{15}+...+\frac{9997}{9999}\)
\(=1-\frac{2}{3}+1-\frac{2}{15}+...+1-\frac{2}{9999}\)
\(=\left(1+1+...+1\right)-\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\right)\)
\(=50-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=50-\left(1-\frac{1}{101}\right)\)
Sau bạn tính tiếp là OK rồi
\(\frac{-3}{15}+\frac{-3}{35}+\frac{-3}{63}+\frac{-3}{99}+\frac{-3}{143}+\frac{-3}{195}\)
\(=\frac{-3}{3.5}+\frac{-3}{5.7}+\frac{-3}{7.9}+\frac{-3}{9.11}+\frac{-3}{11.13}+\frac{-3}{13.15}\)
\(=\frac{-3}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.25}\right)\)
\(=\frac{-3}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{-3}{2}.\left(\frac{1}{3}-\frac{1}{15}\right)=\frac{-3}{2}.\frac{4}{15}=\frac{-2}{5}\)
Đặt \(A=\)\(\frac{1}{15}+\frac{1}{35}+...+\frac{1}{143}\)
\(=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{11.13}\)
\(2A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)
\(2A=\frac{1}{3}-\frac{1}{13}=\frac{10}{39}\)
\(A=\frac{5}{39}\)
Câu còn lại cx dựa như vậy nhé bn !
Chúc bn hc tốt <3
=2/3.5 + 2/5.7 + 2/7.9 + 2/9.11 + 2/11.13
=1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13
= 1/3 - 1/13
= 13/39 -3/39
=10/39
\(\frac{5}{3}+\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+\frac{5}{99}+\frac{5}{143}\)
\(=\frac{5}{2}\cdot\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+...+\frac{2}{11\cdot13}\right)\)
\(=\frac{5}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{5}{2}\cdot\left(1-\frac{1}{13}\right)\)
\(=\frac{5}{2}\cdot\frac{12}{13}\)
\(=\frac{30}{13}\)
\(\frac{5}{3}+\frac{5}{15}+\frac{5}{35}+\frac{5}{63}+\frac{5}{99}+\frac{5}{143}\)
\(=5\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\right)\)
\(=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{5}{2}\left(1-\frac{1}{13}\right)\)
\(=\frac{5}{2}.\frac{12}{13}\)
\(=\frac{30}{13}\)
