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HT
0
A
1
17 tháng 5 2020
Bài này có 2 cách, nhưng cách nào thì cách cx phải dùng tới máy tính, ai cs cách hay show hộ kham khảo !
Cách 1 : cầm máy tính lên bấm
Cách 2 : \(C=\frac{3}{10}+\frac{3}{40}+\frac{3}{88}+\frac{1}{340}\)
\(C=3\left(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}\right)+\frac{1}{340}\)
\(C=3.\frac{3}{22}+\frac{1}{340}=\frac{9}{22}+\frac{1}{340}=\frac{1541}{3740}\)
18 tháng 3 2018
S = 1/2-1/5+1/5-1/8+1/8-...-1/20
S = 1/2-1/20
S = 9/20 nha
LK
18 tháng 3 2018
\(S=\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{17.20}\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-...-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\)
\(=\frac{1}{2}-\frac{1}{20}=\frac{9}{20}\)
ST
2
3 tháng 4 2016
\(A=\frac{3}{10}+\frac{3}{40}+\frac{3}{88}+...+\frac{3}{340}\)
\(=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{17.20}\)
\(=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{17}-\frac{1}{20}\)
\(=\frac{1}{2}-\frac{1}{20}=\frac{9}{20}\)
3 tháng 4 2016
\(\frac{3}{10}+\frac{3}{40}+...+\frac{3}{340}\)
= \(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{17.20}\)
= \(\frac{3}{3}.\left(\frac{1}{2}-\frac{1}{5}+...+\frac{1}{17}-\frac{1}{20}\right)\)
= \(\frac{3}{3}.\left(\frac{1}{2}-\frac{1}{20}\right)\)
= 1. \(\frac{9}{20}\)
= \(\frac{9}{20}\)
N
2
16 tháng 5 2018
\(A=\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+\frac{1}{154}+\frac{1}{238}+\frac{1}{340}\)
\(A=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\)
\(3A=3.\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+\frac{1}{17.20}\right)\)
\(3A=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}\)
\(3A=\frac{5-2}{2.5}+\frac{8-5}{5.8}+\frac{11-8}{8.11}+\frac{14-11}{11.14}+\frac{17-14}{14.17}+\frac{20-17}{17.20}\)
\(3A=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}\)
\(3A=\frac{1}{2}-\frac{1}{20}\)
\(A=\left(\frac{1}{2}-\frac{1}{20}\right)\div3=\frac{9}{20}\div3=\frac{9}{20.3}=\frac{3}{20}\)
Vậy ................
\(B=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot....\cdot\frac{9999}{10000}\)
\(B=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot...\cdot\frac{99.101}{100.100}\)
\(B=\frac{\left(1\cdot2\cdot3\cdot...\cdot99\right).\left(3\cdot4\cdot5\cdot...\cdot101\right)}{\left(2\cdot3\cdot4\cdot...\cdot100\right).\left(2\cdot3\cdot4\cdot...\cdot100\right)}\)
\(B=\frac{1\cdot2\cdot3\cdot..\cdot99}{2\cdot3\cdot4\cdot..\cdot100}\cdot\frac{3\cdot4\cdot5\cdot...\cdot101}{2\cdot3\cdot4\cdot...\cdot100}\)
\(B=\frac{1}{100}\cdot\frac{101}{2}=\frac{101}{200}\)
vậy......
16 tháng 5 2018
A=1/2.5+1/5.8+1/8.11+1/11.14+1/14.17+1/17.20
A=1/3.(3/2.5+3/5.8+3/8.11+3/11.14+3/14.17+3/17.20)
A=1/3.(1/2-1/20)
=3/20
B=1.3/2.2+2.4/3.3+3.5/4.4+...+99.101/100.100
B=(1.2.3...99).(3.4.5...101)/(2.3.4...100).(2.3.4...100)
B=\(\frac{1.2....99}{2.3...100}\).\(\frac{3.4...101}{2.3...100}\)
B=1/100.101/2=101/200
23 tháng 3 2015
4/2.5+4/5.8+4/8.11+..........+4/17.20
=4/3.(3/2.5+3/5.8+3/8.11+...........3/17.20)
=4/3.(1/2-1/5+1/5-1/8+1/8-1/11+...................+1/17-1/20)
=4/3.(1/2-1/20)
=4/3.9/20
=3/5
19 tháng 4 2017
Đặt A=1/10+1/40+1/88+1/154+1/238+1/340
A=1/2.5+1/5.8+1/8.11+1/11.14+1/14.17+1/17.20
3A=3/2.5+3/5.8+....+3/17.20
3A=1/2-1/5+1/5-1/8+...+1/17-1/20
3A=1/2-1/20
3A=9/20
2)
Giữ nguyên p/s 1/2^2
Ta có:1/3^2<1/2.3
1/4^2<1/3.4
...............
1/n^2<1/(n-1).n
=>1/3^2+1/4^2+...+1/n^2<1/2.3+1/3.4+...+1/(n-1).n
=>1/3^2+1/4^2+.....+1/n^2<1/2-1/3+1/3-1/4+.........+1/n-1-1/n
=>1/2^2+1/3^2+.....+1/n^2<1/2^2+1/2-1/n
=>1/2^2+1/3^2+....+1/n^2<3/4-1/n<3/4
3)
2B=2/3.5+2/5.7+....+2/47.49+2/49.51
2B=1/3-1/5+1/5-1/7+.....+1/47-1/49+1/49-1/51
2B=1/3-1/51
2B=16/51
B=16/51:2
B=8/51
19 tháng 4 2017
A=1+1/2+1/2^2+...+1/2^2010
2A=2+1+1/2+....+1/2^2009
2A-A=(2+1+1/2+...+1/2^2009)-(1+1/2+1/2^2+....+1/2^2010)
A=2-1/2^2010
ML
6 tháng 5 2016
S=\(\frac{1}{10}\)+ \(\frac{1}{40}\)+\(\frac{1}{88}\)+\(\frac{1}{154}\)+\(\frac{1}{238}\)+\(\frac{1}{340}\)
S=\(\frac{1}{2.5}\)+\(\frac{1}{5.8}\)+\(\frac{1}{8.11}\)+\(\frac{1}{11.14}\)+\(\frac{1}{14.17}\)+\(\frac{1}{17.20}\)
S= \(\frac{1}{3}\).(\(\frac{3}{2.5}\)+\(\frac{3}{5.8}\)+\(\frac{3}{8.11}\)+\(\frac{3}{11.14}\)+\(\frac{3}{14.17}\)+\(\frac{3}{17.20}\))
S= \(\frac{1}{3}\).(\(\frac{1}{2}\)-\(\frac{1}{20}\))
S= \(\frac{1}{3}\).\(\frac{9}{20}\)
S=\(\frac{3}{20}\)
KQ là 9/20 bạn nha
Chúc bạn học tốt
b = 3/2.5+3/5.8+3/8.11+.....+3/17.20
= 1/2.5+1/5.8+.......+1/17.20
= 1/2-1/5+1/5-1/8+......+1/17-1/20
= 1/2- 1/20
= 9/20