Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
1: \(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{11}-\dfrac{1}{13}\right)\)
=1/2*10/39
=5/39
2: \(=\dfrac{5}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{11}\right)=\dfrac{5}{2}\cdot\dfrac{10}{11}=\dfrac{50}{22}=\dfrac{25}{11}\)
\(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{9}+...+\dfrac{1}{729}\\ =\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^6}\\ =\dfrac{3-1}{2}\cdot\left(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^6}\right)\\ =\dfrac{\left(3-1\right)\left(\dfrac{1}{1}+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^6}\right)}{2}\\ =\dfrac{3-1+1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{3^2}+...+\dfrac{1}{3^5}-\dfrac{1}{3^6}}{2}\\ =\dfrac{3-\dfrac{1}{3^6}}{2}\\ =\dfrac{\dfrac{3^7}{3^6}-\dfrac{1}{3^6}}{2}\\ =\dfrac{2187-1}{729}\cdot\dfrac{1}{2}\\ =\dfrac{2186}{729}\cdot\dfrac{1}{2}\\ =\dfrac{1093}{729}\)
Đặt biểu thức là P , theo bài ra ta có:
\(\dfrac{1}{3}P=\dfrac{1}{3}+\dfrac{1}{3^2}+.......+\dfrac{1}{3^6}+\dfrac{1}{3^7}\)
\(=>P-\dfrac{1}{3}P=\left(1-\dfrac{1}{3^7}\right)\)
\(=>\dfrac{2}{3}P=\dfrac{2186}{2187}\)
\(=>P=\dfrac{2186}{2187}:\dfrac{2}{3}=\dfrac{1093}{729}\)
CHÚC BẠN HỌC TỐT.......
a: \(=\dfrac{1}{9}+\dfrac{13}{4}+5+\dfrac{3}{16}+4+\dfrac{1}{3}+\dfrac{14}{5}+\dfrac{1}{2}\)
\(=9+\dfrac{4}{9}+\dfrac{14}{5}+\dfrac{52}{16}+\dfrac{3}{16}+\dfrac{8}{18}\)
\(=9+\dfrac{146}{45}+\dfrac{63}{16}=\dfrac{11651}{720}\)
b: \(=\dfrac{7}{3}+\dfrac{9}{20}+\dfrac{85}{20}+\dfrac{1}{81}+6+\dfrac{8}{27}\)
\(=6+\dfrac{94}{20}+\dfrac{7\cdot27+1+8\cdot3}{81}\)
\(=6+\dfrac{94}{20}+\dfrac{214}{81}=\dfrac{10807}{810}\)
\(=\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\right)\)
\(=\dfrac{1}{2}\cdot\left(\dfrac{1}{3}-\dfrac{1}{13}\right)=\dfrac{1}{2}\cdot\dfrac{10}{39}=\dfrac{5}{39}\)
`1/15+1/35+1/63+1/99+1/143`
`=1/[3.5]+1/[5.7]+1/[7.9]+1/[9.11]+1/[11.13]`
`=1/2(2/[3.5]+2/[5.7]+2/[7.9]+2/[9.11]+2/[11.13])`
`=1/2.(1/3-1/5+1/5-1/7+...+1/11-1/13)`
`=1/2.(1/3-1/13)`
`=1/2 . 10/39`
`=5/39`
\(\dfrac{1}{3}+\dfrac{1}{27}+\dfrac{1}{81}+\dfrac{1}{243}\)+\(\dfrac{1}{729}\)
=\(\dfrac{243}{729}\)+\(\dfrac{81}{729}\)+\(\dfrac{27}{729}\)+\(\dfrac{3}{729}\)+\(\dfrac{1}{729}\)
=\(\dfrac{355}{729}\)
chúc bạn học tốt ạ