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11 tháng 5 2016

S=1/3.7+1/7.11+...+1/19.23 (1)

Nhân cả 2 vế của đẳng thức (1) với 4 ta được:

4S=4/3.7+4/7.11+...+4/19.23

4S=1/3.7+1/7.11+...+1/19.23

4S=1/3-1/7+1/7-1/11+..+1/19-1/23

4S=1/3-1/23

4S=20/69

S  =20/69:4

S  =5/69

Mọi người ủng hộ mik nha

11 tháng 5 2016

\(S=\frac{1.4}{3.7.4}+\frac{1.4}{7.11.4}+......+\frac{1.4}{19.23.4}\)

     \(=\frac{1}{4}.\left(\frac{4}{3.7}+\frac{4}{7.11}+......+\frac{4}{19.23}\right)\)

     \(=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+......+\frac{1}{19}-\frac{1}{20}\right)\)

      \(=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{20}\right)\)

     \(=\frac{1}{4}.\frac{17}{60}=\frac{17}{240}\)

7 tháng 8 2018

\(\dfrac{4}{3.7}+\dfrac{4}{7.11}+...+\dfrac{4}{23.27}\)

= \(4.\left(\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\text{​​}\dfrac{4}{3.7}+\dfrac{4}{7.11}+...+\dfrac{4}{23.27}\right)\)

=\(1.\left(\dfrac{1}{3.7}+\dfrac{1}{7.11}+...+\dfrac{1}{23.27}\right)\)

= \(1.\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{23}-\dfrac{1}{27}\right)\)

=\(1.\left(\dfrac{1}{3}-\dfrac{1}{27}\right)\)

=\(1.\left(\dfrac{9}{27}-\dfrac{1}{27}\right)\)

= \(1.\dfrac{8}{27}\)

= \(\dfrac{8}{27}\)

mk làm phần a thui nhé

a. A = 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6

A = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6

A =  1/2 - 1/6

A= 3/6 - 1/6

A = 1/3

10 tháng 11 2019

\(B=\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}\)

\(b=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)

\(b=\frac{1}{2}-\frac{1}{14}\)

\(b=\frac{3}{7}\)

\(d=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\)

\(d=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{10\cdot11}\)

\(d=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\)

\(d=1-\frac{1}{11}\)

\(d=\frac{10}{11}\)

\(e=\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)

\(e=\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+\frac{1}{11\cdot14}+\frac{1}{14\cdot17}+\frac{1}{17\cdot20}\)

\(e=\frac{1}{3}\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{17\cdot20}\right)\)

\(e=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\right)\)

\(e=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(e=\frac{1}{3}\cdot\frac{9}{20}=\frac{3}{20}\)

17 tháng 7 2018

\(A=\frac{1}{3.7}+\frac{1}{7.11}+...+\frac{1}{103.107}\)

\(A=\frac{1}{4}.\left(\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{103.107}\right)\)

\(A=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{103}-\frac{1}{107}\right)\)

\(A=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{107}\right)\)

\(A=\frac{1}{4}.\frac{104}{321}\)

\(A=\frac{26}{321}\)

_Chúc bạn học tốt_

17 tháng 7 2018

\(A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{103}-\frac{1}{107}\)

\(A=\frac{1}{3}-\frac{1}{107}=\frac{104}{321}\)

15 tháng 7 2017

\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{23.27}\)

\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}\)

\(=\frac{1}{3}-\frac{1}{27}+0+0+0+0\)

\(=\frac{8}{27}\)

15 tháng 7 2017

Ta có : \(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}+\frac{4}{19.23}+\frac{4}{23.27}\)

\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+.....+\frac{1}{23}-\frac{1}{27}\)

\(=\frac{1}{3}-\frac{1}{27}\)

\(=\frac{8}{27}\)

10 tháng 5 2016

de sai o mau so

10 tháng 5 2016

NEU NHU MINH GIAI DC THI SAO K MINH KO THICH