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7 tháng 6 2018
\(\frac{1}{11\times16}+\frac{1}{16\times21}+\frac{1}{21\times26}+...+\frac{1}{56\times61}+\frac{1}{61\times66}\)
\(=\frac{1}{5}\times\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{56}-\frac{1}{61}+\frac{1}{61}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\times\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\times\frac{5}{66}\)
\(=\frac{1}{66}\)
7 tháng 6 2018
\(\frac{1}{11\times16}+\frac{1}{16\times21}+\frac{1}{21\times26}+...+\frac{1}{56\times61}+\frac{1}{61\times66}\)
\(=\frac{1}{5}\times\left(\frac{5}{11\times16}+\frac{5}{16\times21}+\frac{5}{21\times26}+...+\frac{5}{56\times61}+\frac{5}{61\times66}\right)\)
\(=\frac{1}{5}\times\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{56}-\frac{1}{61}+\frac{1}{61}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\times\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\times\frac{5}{66}=\frac{1}{66}\)
26 tháng 2 2017
đặt A= dãy số trên.Ta có:
5A= \(\frac{5}{11x16}+\frac{5}{16x21}+...+\frac{5}{61x66}\)
=> 5A= \(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
=> 5A = \(\frac{1}{11}-\frac{1}{66}\)
=> 5A= \(\frac{5}{66}\)
=> A=\(\frac{1}{66}\)
VV
26 tháng 2 2017
\(=\frac{1}{5}\left(\frac{5}{11.16}\frac{5}{16.21}\frac{5}{21.26}+......+\frac{5}{61.66}\right)\)
\(=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+....+\frac{1}{61}+\frac{1}{66}\right)\)
=\(\frac{1}{5}\left(\frac{1}{11}+\frac{1}{66}\right)\)
\(=\frac{1}{5}.\frac{7}{66}\)
\(=\frac{7}{330}\)
8 tháng 6 2023
`@` `\text {Ans}`
`\downarrow`
\(\text{ A = }\dfrac{1}{4\times8}+\dfrac{1}{8\times12}+\dfrac{1}{12\times16}+...+\dfrac{1}{172\times176}\)
\(\text{A = }\dfrac{1}{4}\times\left(\dfrac{4}{4\times8}+\dfrac{4}{12\times16}+...+\dfrac{4}{172\times176}\right)\)
\(\text{A = }\dfrac{1}{4}\times\left(\dfrac{1}{4}-\dfrac{1}{8}+\dfrac{1}{12}-\dfrac{1}{16}+...+\dfrac{1}{172}-\dfrac{1}{176}\right)\)
\(\text{A = }\dfrac{1}{4}\times\left(\dfrac{1}{4}-\dfrac{1}{176}\right)\)
\(\text{A = }\dfrac{1}{4}\times\dfrac{43}{176}\)
\(\text{A = }\dfrac{43}{704}\)
Đáp số: `\text {A =} 43/704.`
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
6 tháng 6 2023
A = \(\dfrac{1}{4\times8}\) + \(\dfrac{1}{8\times12}\) + \(\dfrac{1}{12\times16}\) +...+ \(\dfrac{1}{176\times180}\)
A = \(\dfrac{1}{4}\) \(\times\)( \(\dfrac{4}{4\times8}\)+ \(\dfrac{4}{12\times16}\)+...+ \(\dfrac{4}{176\times180}\))
A = \(\dfrac{1}{4}\) \(\times\)( \(\dfrac{1}{4}\) - \(\dfrac{1}{8}\) + \(\dfrac{1}{12}\) - \(\dfrac{1}{16}\) +...+ \(\dfrac{1}{176}\) - \(\dfrac{1}{180}\))
A = \(\dfrac{1}{4}\) \(\times\)(\(\dfrac{1}{4}\) - \(\dfrac{1}{180}\))
A = \(\dfrac{1}{4}\) \(\times\)\(\dfrac{11}{45}\)
A = \(\dfrac{11}{180}\)
8 tháng 6 2023
A = 1/4 x 8 + 1/8 x 12 + 1/12 x 16 + ... + 1/176 x 180
=> 4A = 4/4 x 8 + 4/8 x 12 + 4/12 x 16 + ... + 4/176 x 180
=> 4A = 1/4 - 1/8 + 1/8 - 1/12 + 1/12 - 1/16 + ... 1/176 - 1/180
=> 4A = 1/4 - 1/180
=> 4A = 45/180 - 1/180
=> 4A = 44/180
=> 4A = 11/45
=> A = 11/45 : 4
=> A = 11/180
Vậy A = 11/180
31 tháng 7 2016
\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(x-10.\frac{4}{55}=\frac{3}{11}\)
\(x-\frac{40}{55}=\frac{3}{11}\)
\(x=\frac{3}{11}+\frac{40}{55}\)
\(x=\frac{55}{55}=1\)
nha.
Dấu " . " là dấu nhân
\(\frac{16\cdot17-5}{16\cdot16+11}\)
\(=\frac{16\cdot\left(16+1\right)-5}{16^2+11}\)
\(=\frac{16^2+16-5}{16^2+11}\)
\(=\frac{16^2+11}{16^2+11}\)
\(=1\)
\(\frac{16\times17-5}{16\times16+11}=\frac{16\times\left(16+1\right)-5}{16\times16+11}=\frac{16\times16+16-5}{16\times16+11}=1\)