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NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
26 tháng 6 2023
A = \(\dfrac{5}{1.6}\)+\(\dfrac{5}{6.11}\)+\(\dfrac{5}{11.16}\)+\(\dfrac{5}{16.21}\)+...+\(\dfrac{5}{101.106}\)
A = \(\dfrac{1}{1}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{101}-\dfrac{1}{106}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{106}\)
A = \(\dfrac{105}{106}\)
B = \(\dfrac{3}{1.4}\) +\(\dfrac{3}{4.7}\)+\(\dfrac{3}{7.10}\)+...+\(\dfrac{3}{97.100}\)
B = \(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{97}-\dfrac{1}{100}\)
B = \(\dfrac{1}{1}\) - \(\dfrac{1}{100}\)
B = \(\dfrac{99}{100}\)
C = \(\dfrac{1}{2.7}+\dfrac{1}{7.12}\) + \(\dfrac{1}{12.17}\)+...+ \(\dfrac{1}{97.102}\)
C= \(\dfrac{1}{5}\) \(\times\)( \(\dfrac{5}{2.7}+\dfrac{5}{7.12}+\dfrac{5}{12.17}+...+\dfrac{5}{97.102}\))
C = \(\dfrac{1}{5}\)\(\times\)(\(\dfrac{1}{2}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{12}\) + \(\dfrac{1}{12}\) - \(\dfrac{1}{17}\)+...+ \(\dfrac{1}{97}\) - \(\dfrac{1}{102}\))
C = \(\dfrac{1}{5}\) \(\times\)( \(\dfrac{1}{2}\) - \(\dfrac{1}{102}\))
C = \(\dfrac{1}{5}\) \(\times\) \(\dfrac{25}{51}\)
C = \(\dfrac{5}{51}\)
D = \(\dfrac{1}{2}\) + \(\dfrac{1}{6}\) + \(\dfrac{1}{12}\) + \(\dfrac{1}{20}\) + \(\dfrac{1}{30}\) + \(\dfrac{1}{42}\) + \(\dfrac{1}{56}\) + \(\dfrac{1}{72}\)
D = \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{4.5}\) + \(\dfrac{1}{5.6}\) + \(\dfrac{1}{6.7}\)+\(\dfrac{1}{7.8}\)+ \(\dfrac{1}{8.9}\)
D = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\)+\(\dfrac{1}{2}\)-\(\dfrac{1}{3}\)+\(\dfrac{1}{3}\)-\(\dfrac{1}{4}\)+\(\dfrac{1}{4}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{6}\)+\(\dfrac{1}{6}\) - \(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{8}\)+\(\dfrac{1}{8}\)-\(\dfrac{1}{9}\)
D = \(\dfrac{1}{1}\) - \(\dfrac{1}{9}\)
D = \(\dfrac{8}{9}\)
E = \(\dfrac{3}{2.4}\)+\(\dfrac{3}{4.6}\)+\(\dfrac{3}{6.8}\)+...+\(\dfrac{3}{98.100}\)
E = \(\dfrac{3}{2}\) \(\times\) ( \(\dfrac{2}{2.4}\) + \(\dfrac{2}{4.6}\)+ \(\dfrac{2}{6.8}\)+...+\(\dfrac{2}{98.100}\))
E = \(\dfrac{3}{2}\)\(\times\)( \(\dfrac{1}{2}\) - \(\dfrac{1}{4}\)+ \(\dfrac{1}{4}\) - \(\dfrac{1}{6}\)+\(\dfrac{1}{6}\)-\(\dfrac{1}{8}\)+...+\(\dfrac{1}{98}\) - \(\dfrac{1}{100}\))
E = \(\dfrac{3}{2}\) \(\times\) ( \(\dfrac{1}{2}\) - \(\dfrac{1}{100}\))
E = \(\dfrac{3}{2}\) \(\times\) \(\dfrac{49}{100}\)
E = \(\dfrac{147}{200}\)
DD
1
25 tháng 7 2016
\(\frac{2}{1x6}+\frac{2}{6x11}+\frac{2}{11x16}+\frac{2}{16x21}+\frac{2}{21x26}\)
= \(\frac{2}{6}+\frac{2}{66}+\frac{2}{176}+\frac{2}{336}+\frac{2}{546}\)
= \(\frac{1}{3}+\frac{1}{33}+\frac{1}{88}+\frac{1}{168}+\frac{1}{273}\)
=\(\frac{5}{13}\)
Mình tự nghĩ đấy .
Chúc bạn học tốt!
QM
2
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
27 tháng 4 2023
A = \(\dfrac{25}{1\times6}\) + \(\dfrac{25}{6\times11}\) + \(\dfrac{25}{11\times16}\)+\(\dfrac{25}{16\times21}\)+ \(\dfrac{25}{26\times31}\)
A = 5 \(\times\) ( \(\dfrac{5}{1\times6}\)+\(\dfrac{5}{6\times11}\)+\(\dfrac{5}{11\times16}\)+\(\dfrac{5}{16\times21}\)+\(\dfrac{5}{26\times31}\))
A = 5 \(\times\) ( \(\dfrac{1}{1}\) - \(\dfrac{1}{6}\) + \(\dfrac{1}{6}\) - \(\dfrac{1}{11}\)+ \(\dfrac{1}{11}\)- \(\dfrac{1}{16}\)+ \(\dfrac{1}{16}\)- \(\dfrac{1}{21}\)+ \(\dfrac{1}{26}\)- \(\dfrac{1}{31}\))
A = 5 \(\times\)( 1 - \(\dfrac{1}{31}\))
A = 5 \(\times\) \(\dfrac{30}{31}\)
A = \(\dfrac{150}{31}\)
19 tháng 11 2017
Đặt \(A=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{496.501}\)
\(\Rightarrow5A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{496}+\frac{1}{501}\)
\(\Rightarrow5A=1-\frac{1}{501}=\frac{500}{501}\)
\(\Rightarrow A=\frac{500}{501}:5=\frac{500}{501}.\frac{1}{5}=\frac{100}{501}\)
19 tháng 11 2017
k mik nhé
=1/5x(1-1/6+1/6-1/11-1/16+...+1/496-1/501
=1/5x(1-1/501)
=1/5x500/501
=100/501
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
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)-\frac{1}{21}\)
\(=\frac{1}{11}-\frac{1}{21}\)
\(=\frac{21}{231}-\frac{11}{231}\)
\(=\frac{10}{231}\)
DG
1
S
23 tháng 9 2023
\(E=\dfrac{1}{1\times2}+\dfrac{2}{2\times4}+\dfrac{3}{4\times7}+\dfrac{4}{7\times11}+\dfrac{5}{11\times16}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}\)
\(=1-\dfrac{1}{16}=\dfrac{15}{16}\)
#kễnh
DN
1
20 tháng 10 2015
A=1/1-1/2+1/2-1/4+1/4-1/7+1/7-1/11+1/11-1/16+1/16-1/22+1/22-1/29
A=1/1-1/29
A=28/29
VT
1
17 tháng 9 2017
Ta có : \(C=\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+......+\frac{2}{41.42}\)
\(C=2\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{41.42}\right)\)
\(C=2\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{41}-\frac{1}{42}\right)\)
\(C=2\left(\frac{1}{3}-\frac{1}{42}\right)\)
\(C=2.\frac{13}{42}=\frac{13}{21}\)