B=1/16+1/15+1/21+...+1/120
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S
1 tháng 7 2018
\(\frac{1}{2}B=\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\)
\(\frac{1}{2}B=\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{15.16}\)
\(\frac{1}{2}B=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\)
\(\frac{1}{2}B=\frac{1}{4}-\frac{1}{16}=\frac{3}{16}\Rightarrow B=\frac{3}{16}:\frac{1}{2}=\frac{3}{8}\)
1 tháng 7 2018
\(B=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(B=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)
\(B=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(B=2\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(B=2.\frac{3}{16}=\frac{6}{16}=\frac{3}{8}\)
VH
0
MN
4 tháng 2 2018
a) \(\frac{3}{16}+\frac{4}{15}+\frac{5}{16}+\frac{1}{15}\)
\(=\left(\frac{3}{16}+\frac{5}{16}\right)+\left(\frac{4}{15}+\frac{1}{15}\right)\)
\(=\frac{1}{2}+\frac{1}{3}\)
\(=\frac{5}{6}\)
b) \(\frac{6}{7}\times\frac{8}{15}\times\frac{7}{6}\times\frac{15}{16}\)
\(=\left(\frac{6}{7}\times\frac{7}{6}\right)\times\left(\frac{8}{15}\times\frac{15}{16}\right)\)
\(=1\times\frac{1}{2}=\frac{1}{2}\)
c) \(\frac{19}{20}\times\frac{13}{21}+\frac{9}{20}\times\frac{8}{21}\)
\(=\frac{19\times13}{20\times21}+\frac{9\times8}{20\times21}\)
\(=\frac{247}{420}+\frac{72}{420}\)
\(=\frac{319}{420}\)
TT
2
7 tháng 7 2016
Ta có: \(B=\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\)
\(\Rightarrow B=\frac{2}{20}+\frac{2}{30}+...+\frac{2}{240}\)
\(\Rightarrow B=2.\left(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{15.16}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{4}-\frac{1}{16}\right)=2.\frac{3}{16}=\frac{3}{8}\)
Vậy \(B=\frac{3}{8}\)
nha m.n
VA
7 tháng 7 2016
\(B=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+.....+\frac{1}{120}\)
\(B=2.\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+.....+\frac{1}{240}\right)\)
\(B=2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)
\(B=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+......+\frac{1}{15}-\frac{1}{16}\right)\)
\(B=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(B=2.\frac{3}{16}\)
\(B=\frac{3}{8}\)
Vậy \(B=\frac{3}{8}\)
MN
1
3 tháng 7 2015
1/10+1/15+1/21+...+1/120
=2*(1/20+1/30+1/42+...+1/240)
=2*(1/4*5+1/5*6+...+1/15*16)
=2*(1/4-1/5+1/5-1/6+...+1/15-1/16)
=2*[(1/4-1/16)+(1/5-1.5)+...+(1/15-1/15)]
=2[(4/16-1/16)+0+...+0]]
=2*3/16=3/8
TV
2
24 tháng 9 2021
\(S=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)
\(S=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+....+\frac{2}{240}\)
\(2S=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{240}\)
\(2S=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+.....+\frac{1}{15.16}\)
\(2S=\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)+.....+\left(\frac{1}{15}-\frac{1}{16}\right)\)
\(2S=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{15}-\frac{1}{16}\)
\(2S=\frac{1}{4}-\frac{1}{16}\)
\(2S=\frac{3}{16}\)
\(S=\frac{3}{8}\)
LT
1
D
2 tháng 5 2015
Đặt A = \(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)
=> A = \(2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{240}\right)\)
= \(2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)
= \(2\left(\frac{1}{4}-\frac{1}{16}\right)=2\left(\frac{4}{16}-\frac{1}{16}\right)=2.\frac{3}{16}=\frac{3}{8}\)
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