tính giá trị của biểu thức
E=1/3+1/6+1/10+1/15+1/21+1/28+1/36
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TT
0
11 tháng 2 2017
ta có
1/2 P=1/2(1-1/10-1/15-1/3-1/28-1/6-1/21)
=1/2-(1/6+1/12+1/20+1/30+1/42+1/56)
=1/2-(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8)
=1/2-(1/2-1/8)
=1/8
suy ra P=1/4
11 tháng 2 2017
ta có
1/2 P=1/2(1-1/10-1/15-1/3-1/28-1/6-1/21)
=1/2-(1/6+1/12+1/20+1/30+1/42+1/56)
=1/2-(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8)
=1/2-(1/2-1/8)
=1/8
suy ra P=1/4
HT
0
2 tháng 4 2017
21)
\(\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{8}\right).\left(1+\dfrac{1}{15}\right).....\left(1+\dfrac{1}{9999}\right)\\ =\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.....\dfrac{10000}{9999}\\ =\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.\dfrac{4.4}{3.5}.....\dfrac{100.100}{99.101}\\ =\dfrac{2.3.4.....100}{1.2.3.....99}.\dfrac{2.3.4.....100}{3.4.5.....101}\\ =100.\dfrac{2}{101}\\ =\dfrac{200}{101}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
19 tháng 5 2023
A = 1 + \(\dfrac{1}{3}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{10}\) + \(\dfrac{1}{15}\) + \(\dfrac{1}{21}\) + \(\dfrac{1}{28}\) + \(\dfrac{1}{36}\)
A = 2\(\times\) ( \(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\) + \(\dfrac{1}{42}\) + \(\dfrac{1}{56}\)+ \(\dfrac{1}{72}\))
A =2\(\times\)( \(\dfrac{1}{1\times2}\)+\(\dfrac{1}{2\times3}\)+\(\dfrac{1}{3\times4}\)+\(\dfrac{1}{4\times5}\)+\(\dfrac{1}{5\times6}\)+\(\dfrac{1}{6\times7}\)+\(\dfrac{1}{7\times8}\)+\(\dfrac{1}{8\times9}\))
A = 2 \(\times\) ( \(\dfrac{1}{1}\)- \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+...+\(\dfrac{1}{8}\)-\(\dfrac{1}{9}\))
A = 2\(\times\)( 1 - \(\dfrac{1}{9}\))
A = 2 \(\times\) \(\dfrac{8}{9}\)
A = \(\dfrac{16}{9}\)
LC
3
8 tháng 8 2020
Bài làm:
Ta có: \(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{66}\)
\(=\frac{1}{1}+\frac{1}{1.3}+\frac{1}{3.2}+...+\frac{1}{11.6}\)
\(=\frac{1}{2}\left(\frac{1}{1.2}+\frac{1}{2.1.3}+\frac{1}{2.3.2}+...+\frac{1}{2.11.6}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{11.12}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{12}\right)\)
\(=\frac{1}{2}.\frac{11}{12}\)
\(=\frac{11}{24}\)
NH
8 tháng 8 2020
\(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+\frac{1}{55}+\frac{1}{66}\)
\(=\frac{2}{2}+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+...+\frac{2}{90}+\frac{2}{110}+\frac{2}{132}\)
\(=2\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{9\times10}+\frac{1}{10\times11}+\frac{1}{11\times12}\right)\)
\(=2\times\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\right)\)
\(=2\times\left(1-\frac{1}{12}\right)\)
\(=2\times\frac{11}{12}\)
\(=\frac{11}{6}\)
\(\frac{1}{2}\) E= \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)
\(\frac{1}{2}\) E = \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\)
\(\frac{1}{2}E\) = \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\)
\(\frac{1}{2}E\) = \(\frac{1}{2}-\frac{1}{9}\)
\(\frac{1}{2}E\) =\(\frac{7}{18}\)
=> E = \(\frac{7}{9}\)
E=\(\frac{1}{3}+\frac{1}{6}+....+\frac{1}{28}+\frac{1}{36}\)
\(\frac{1}{2}E=\frac{1}{6}+\frac{1}{12}+...+\frac{1}{56}+\frac{1}{72}\)
\(\frac{1}{2}E=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{7.8}+\frac{1}{8.9}\)
\(\frac{1}{2}E=\frac{3-2}{2.3}+\frac{4-3}{3.4}+...\frac{8-7}{7.8}+\frac{9-8}{8.9}\)
\(\frac{1}{2}E=\frac{3}{2.3}-\frac{2}{2.3}+\frac{4}{3.4}-\frac{3}{3.4}+...+\frac{8}{7.8}-\frac{7}{7.8}+\frac{9}{8.9}-\frac{8}{8.9}\)
\(\frac{1}{2}E=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
\(\frac{1}{2}E=\frac{1}{2}-\frac{1}{9}=\frac{7}{18}\)
E=\(\frac{7}{18}:\frac{1}{2}=\frac{7}{9}\)