tinh:
A=\(\frac{1}{3}+\frac{1}{7}-\frac{1}{55}\):\(\frac{1}{3}+\frac{1}{7}-\frac{1}{55}+\frac{1}{3}.\frac{1}{7}.\frac{1}{55}+\frac{1}{55.9+35}\)
K
Khách
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NP
1
27 tháng 12 2018
\(A=\frac{3^2-1}{5^2-1}:\frac{9^2-1}{7^2-1}:\frac{13^2-1}{11^2-1}:...:\frac{55^2-1}{53^2-1}\)
\(=\frac{\left(3-1\right)\left(3+1\right)}{\left(5-1\right)\left(5+1\right)}:\frac{\left(9-1\right)\left(9+1\right)}{\left(7-1\right)\left(7+1\right)}:\frac{\left(13-1\right)\left(13+1\right)}{\left(11-1\right)\left(11+1\right)}:...:\frac{\left(55-1\right)\left(55+1\right)}{\left(53-1\right)\left(53+1\right)}\)
\(=\frac{2.4}{4.6}:\frac{8.10}{6.8}:\frac{12.14}{10.12}:...:\frac{54.56}{52.54}\)
\(=\frac{2.4.6.8.10.12......52.54}{4.6.8.10.12.....54.56}\)
\(=\frac{2}{56}\)
\(=\frac{1}{28}\)
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)
\(=1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+\frac{2}{90}+\frac{2}{110}+\frac{2}{132}\)
\(=1+\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+\frac{2}{9.10}+\frac{2}{10.11}+\frac{2}{11.12}\)
\(...\)
NH
14 tháng 3 2018
Giup tui voi !!!!!!!!!!!!!!!!!!!!!!!!!!! Mai phai nop roi !!!!!!!!!!!!!!!!!!!
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
S
1