tính nhanh: 1/6 + 1/24 +1/60 +... + 1/970200
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12 tháng 3 2020
\(A=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{18\cdot19\cdot20}\)
\(A=\frac{1}{2}\cdot\frac{2}{1\cdot2\cdot3}+\frac{1}{2}\cdot\frac{2}{2\cdot3\cdot4}+\frac{1}{2}\cdot\frac{2}{3\cdot4\cdot5}+...+\frac{1}{2}\cdot\frac{2}{18\cdot19\cdot20}\)
\(A=\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{18\cdot19\cdot20}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2.3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{18\cdot19}-\frac{1}{19\cdot20}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{2}-0-0-...-0-\frac{1}{380}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{380}\right)\)
\(A=\frac{1}{2}\cdot\frac{189}{380}\)
\(A=\frac{189}{760}\)
HV
1
B
2
25 tháng 7 2015
Cho tg tren la A
A=\(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}\)
\(A=2\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{14}\right)\)
\(A=2.\frac{3}{7}\)
\(A=\frac{6}{7}\)
VT
13 tháng 12 2024
A = 1/4 + 1/12 + 1/24 + 1/40 + 1/60 + 1/84
= 2 ( 1/2*4 + 1/4*6 + 1/6*8 + 1/8*10 + 1/10*12 + 1/12*14 )
= 2 ( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + 1/8 - 1/10 + 1/10 - 1/12 + 1/12 - 1/14 )
= 2 ( 1/2 - 1/14 )
= 6/7
ND
1
25 tháng 7 2015
Ta co :
\(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}\)
\(=2\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{14}\right)\)
\(=2.\frac{3}{7}\)
\(=\frac{6}{7}\)
B
6
25 tháng 7 2015
Đặt A = 1/4 + ... +1/84
A = 2/8 + 2/24 + ... + 2/168
A = 2/2.4 + 2/4.6 + ... + 2/12.14
A = 1/2 - 1/4 + 1/4 - 1/6 + .. + 1/12 - 1/14
A = 1/2 - 1/14
A = 6/14 = 3/7
25 tháng 7 2015
\(A=\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}\)
\(A=\frac{2}{8}+\frac{2}{24}+\frac{2}{48}+\frac{2}{80}+\frac{2}{120}+\frac{2}{168}\)
\(A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}+\frac{2}{12.14}\)
\(A=\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{8}\right)+\left(\frac{1}{8}-\frac{1}{10}\right)+\left(\frac{1}{10}-\frac{1}{12}\right)+\left(\frac{1}{12}-\frac{1}{14}\right)\)
\(A=\frac{1}{2}-\frac{1}{14}\)
\(A=\frac{3}{7}\)
Vậy \(\frac{1}{4}+\frac{1}{12}+\frac{1}{24}+\frac{1}{40}+\frac{1}{60}+\frac{1}{84}=\frac{3}{7}\)
NT
0
HV
1
HN
9 tháng 1 2022
\( \begin{array}{l} \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{6} +\frac{1}{12} +\frac{1}{20} +...+\frac{1}{240}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2.3} +\frac{1}{3.4} +\frac{1}{4.5} +...+\frac{1}{15.16}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{3} +\frac{1}{3} -\frac{1}{4} +...+\frac{1}{15} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\frac{7}{16}\\ \Leftrightarrow \ B=\frac{7}{32} \end{array}\)
HV
1
HN
9 tháng 1 2022
\( \begin{array}{l} \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{6} +\frac{1}{12} +\frac{1}{20} +...+\frac{1}{240}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2.3} +\frac{1}{3.4} +\frac{1}{4.5} +...+\frac{1}{15.16}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{3} +\frac{1}{3} -\frac{1}{4} +...+\frac{1}{15} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\frac{7}{16}\\ \Leftrightarrow \ B=\frac{7}{32} \end{array}\)
TA
2
10 tháng 8 2023
`d,E = 4.5 - (20^2 + 1)(20^2 - 1)`
`=21 - 20^4`
`=-159979`
`f,64^2 + 24^2 - 60^2 - 48.64`
`=64(64 - 48) + 24^2 - 60^2`
`=64. 16 + 24^2 - 60^2`
`=1024 + 576 - 3600`
`=1600 - 3600`
`=-2000`
10 tháng 8 2023
d: =20-(20^4-1)
=20-20^4+1
=21-20^4
=-159979
f: =(64-24)^2-60^2
=40^2-60^2
=-20*100=-2000
NK
0
A=61+241+601+...+9702001
�=11.2.3+12.3.4+13.4.5+...+198.99.100A=1.2.31+2.3.41+3.4.51+...+98.99.1001
Ta có:
11.2.3=12(11.2−12.3)1.2.31=21(1.21−2.31);
12.3.4=12(12.3−13.4)2.3.41=21(2.31−3.41);
...;
198.99.100=12(198.99−199.100)98.99.1001=21(98.991−99.1001)
�=12(11.2−12.3+12.3−13.4+...+198.99−199.100)A=21(1.21−2.31+2.31−3.41+...+98.991−99.1001)
�=12(11.2−199.100)A=21(1.21−99.1001)
�=12(99.100−2200.99)A=21(200.9999.100−2)
�=12(98998200.99)=4949919800A=21(200.9998998)=1980049499