Tính nhanh
\(C=\frac{1}{11X16}+\frac{1}{16x21}+\frac{1}{21x26}+...\frac{1}{56x61}+\frac{1}{61x66}\)
K
Khách
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Những câu hỏi liên quan
DN
2
AV
8 tháng 7 2019
E=\(\frac{1}{5}\).(\(\frac{1}{11}-\frac{1}{16}\)+\(\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+....+\frac{1}{61}-\frac{1}{66}\))
E=\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)=\(\frac{1}{5}.\frac{5}{66}=\frac{1}{66}\)
8 tháng 7 2019
\(E=\frac{1}{11x16}+\frac{1}{16x21}+\frac{1}{21x26}+...+\frac{1}{61x66}\)
\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(E=\frac{1}{5}.\frac{5}{66}\)
\(E=\frac{1}{66}\)
17 tháng 9 2017
Ta có : \(C=\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+......+\frac{2}{41.42}\)
\(C=2\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{41.42}\right)\)
\(C=2\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{41}-\frac{1}{42}\right)\)
\(C=2\left(\frac{1}{3}-\frac{1}{42}\right)\)
\(C=2.\frac{13}{42}=\frac{13}{21}\)
TM
4
8 tháng 7 2017
\(\frac{5}{11x16}+\frac{5}{16x21}+...+\frac{5}{61x66}\)
\(=\frac{5}{11}-\frac{5}{16}+\frac{5}{16}-\frac{5}{21}+...+\frac{5}{61}-\frac{5}{66}\)
\(=\frac{5}{11}-\frac{5}{66}+0+...+0\)
\(=\frac{25}{66}\)
~ Ủng hộ nhé anh chị em ~
NL
8 tháng 7 2017
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)-\frac{1}{21}\)
\(=\frac{1}{11}-\frac{1}{21}\)
\(=\frac{21}{231}-\frac{11}{231}\)
\(=\frac{10}{231}\)
19 tháng 7 2016
\(A=11\left(\frac{5}{11.6}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)
\(=11\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.....+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(=11.\frac{30}{451}=\frac{30}{41}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
13 tháng 8 2023
Bài 1:
A = \(\dfrac{1}{1\times3}\) + \(\dfrac{1}{3\times5}\) + \(\dfrac{1}{5\times7}\) +...+ \(\dfrac{1}{2019\times2021}\)
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{2}{1\times3}\) + \(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\)+...+ \(\dfrac{2}{2019\times2021}\))
A = \(\dfrac{1}{2}\) \(\times\)( \(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\)+...+ \(\dfrac{1}{2019}\) - \(\dfrac{1}{2021}\))
A = \(\dfrac{1}{2}\) \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{2021}\))
A = \(\dfrac{1010}{2021}\)
HT
14 tháng 7 2015
\(\frac{55}{16.21}\)chứ nhỉ.
A=\(\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+\frac{55}{26.31}+\frac{55}{31.36}+\frac{55}{36.41}\)
A= 11.\(\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+....+\frac{1}{36}-\frac{1}{41}\right)\)
A= 11\(\left(\frac{1}{11}-\frac{1}{41}\right)\)
A= 11.\(\frac{30}{451}\)
A= \(\frac{30}{41}\)
5 tháng 6 2017
\(A=\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+......+\frac{55}{36.41}\)
\(=11\left(\frac{5}{11.16}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.......+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(=11.\frac{30}{451}=\frac{30}{41}\)
27 tháng 4 2019
\(S=\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+\frac{5^2}{16\cdot21}+\frac{5^2}{21\cdot26}\)
\(S=\frac{25}{1\cdot6}+\frac{25}{6\cdot11}+\frac{25}{11\cdot16}+\frac{25}{16\cdot21}+\frac{25}{21\cdot26}\)
\(S=5\left[\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+\frac{5}{21\cdot26}\right]\)
\(S=5\left[1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right]\)
\(S=5\left[1-\frac{1}{26}\right]=5\cdot\frac{25}{26}=\frac{125}{26}\)
27 tháng 4 2019
Bài làm
S = \(\frac{5^2}{1.6}\)+ \(\frac{5^2}{6.11}\)+ \(\frac{5^2}{11.16}\)+ \(\frac{5^2}{16.21}\)+\(\frac{5^2}{21.26}\)
S : 5 = \(\frac{5}{1.6}\)+ \(\frac{5}{6.11}\)+ \(\frac{5}{11.16}\) + \(\frac{5}{16.21}\) + \(\frac{5}{21.26}\)
S : 5 = 1 - \(\frac{1}{6}\)+ \(\frac{1}{6}\)- \(\frac{1}{11}\) + \(\frac{1}{11}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{21}\)+ \(\frac{1}{21}\)- \(\frac{1}{26}\)
S : 5 = 1 - \(\frac{1}{26}\)
S : 5 = \(\frac{25}{26}\)
S = \(\frac{125}{26}\)
6 tháng 7 2016
\(C=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x...x\frac{9999}{10000}\)
\(C=\frac{3}{4}x\frac{4x2}{3x3}x\frac{3x5}{2x8}x...x\frac{99x101}{100x100}\)
\(C=...\) ( Tự làm tiếp )
\(E=1\frac{1}{3}x1\frac{1}{8}x1\frac{1}{15}x1\frac{1}{24}x...x1\frac{1}{99}\)
\(E=\frac{4}{3}x\frac{9}{8}x\frac{16}{15}x\frac{25}{24}x...x\frac{100}{99}\)
\(E=....\)( tương tự câu C )
\(C=\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}=\frac{5}{5}\cdot\left(\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}\right)\)
\(=\frac{1}{5}\cdot\left(\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+...+\frac{5}{61\cdot66}\right)=\frac{1}{5}\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\cdot\left[\left(\frac{1}{11}-\frac{1}{66}\right)+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)\right]\)
\(=\frac{1}{5}\cdot\left[\left(\frac{6}{66}-\frac{1}{66}\right)+0+...+0\right]=\frac{1}{5}\cdot\frac{5}{66}=\frac{1\cdot5}{5\cdot66}=\frac{1\cdot1}{1\cdot66}=\frac{1}{66}\)
Vậy \(C=\frac{1}{66}\)
Chúc bạn học tốt!^_^