a, \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{1}{306}\)
b, \(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
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18 tháng 1 2017
lấy (1/3 + 1/15 +1/10 + 1/21 ) + (1/36 + 1/28 + 1/6) + (1/45 + 1/55)
= (4/50 + 3/70) + 2/100
= 7/120 + 2/100
= 9/220
2 tháng 4 2017
21)
\(\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{8}\right).\left(1+\dfrac{1}{15}\right).....\left(1+\dfrac{1}{9999}\right)\\ =\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.....\dfrac{10000}{9999}\\ =\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}.\dfrac{4.4}{3.5}.....\dfrac{100.100}{99.101}\\ =\dfrac{2.3.4.....100}{1.2.3.....99}.\dfrac{2.3.4.....100}{3.4.5.....101}\\ =100.\dfrac{2}{101}\\ =\dfrac{200}{101}\)
BG
0
NL
3
LT
16 tháng 4 2017
p=1-1/2.5-1/3.5-1/1.3-1/4.7-1/2.3-1/3.7
p=1-(1/2.1/5-1/3.1/5)-(1/1.1/3-1/2.1/3)-(1/4.1/7-1/3.1/7)
p=1-(1/5.(1/2-1/3))-(1/3.(1-1/2))-(1/7.(1/4-1/3)
p=1-(1/5.1/6)-(1/3.1/2)-(1/7.-1/12)
p=1-1/30-1/6+1/84
p=341/420
22 tháng 5 2017
\(=1+\frac{1}{1.3}+\frac{1}{3.2}+\frac{1}{2.5}+\frac{1}{5.3}+\frac{1}{3.7}+\frac{1}{7.4}+\frac{1}{4.9}+\frac{1}{9.5}\)
\(=1+1-\frac{1}{5}\)
\(=\frac{10}{5}-\frac{1}{5}\)
\(=\frac{9}{5}\)
Ai thấy đúng thì
NM
24 tháng 3 2019
a) \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\frac{14}{15}\)
\(=\frac{14}{30}=\frac{7}{15}\)
LN
24 tháng 3 2019
a)
\(=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=2\left(1-\frac{1}{15}\right)\)
\(=2.\frac{14}{15}\)
\(=\frac{28}{15}\)
b)
\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}+\frac{2}{110}+\frac{2}{132}\)
\(=1+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+\frac{2}{9.10}+\frac{2}{10.11}+\frac{2}{11.12}\)
\(...\)
21 tháng 4 2018
A=1+(1/6+1/12+1/20+...+1/90):2
A=1+(1/2-1/3+1/3-1/4+1/4-1/5+...+1/9-1/10):2
A=1+(1/2-1/10):2
A=1+2/5:2
A=1+1/5
A=6/5
Vậy A=6/5 nha bạn
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