1/10+1/15+1/21+......+1/120 = ?
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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
24 tháng 9 2021
\(S=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)
\(S=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+....+\frac{2}{240}\)
\(2S=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{240}\)
\(2S=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+.....+\frac{1}{15.16}\)
\(2S=\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)+.....+\left(\frac{1}{15}-\frac{1}{16}\right)\)
\(2S=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{15}-\frac{1}{16}\)
\(2S=\frac{1}{4}-\frac{1}{16}\)
\(2S=\frac{3}{16}\)
\(S=\frac{3}{8}\)
12 tháng 5 2016
Đặt A=1/10+1/15+1/21+...+1/120
1/2 A=1/20+1/30+1/42+...+1/240
A=1/4-1/5+1/5-1/6+1/6-1/7+...+1/15-1/16
A=1/4-1/16
A=3/16
Vậy:1/10+1/15+1/21+...+1/120=3/16
12 tháng 5 2016
\(C=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}=2\times\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(C=2\times\left(\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+...+\frac{1}{15\times16}\right)\)
\(C=2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)=2\times\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{3}{8}\)
7 tháng 7 2016
Ta có: \(B=\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\)
\(\Rightarrow B=\frac{2}{20}+\frac{2}{30}+...+\frac{2}{240}\)
\(\Rightarrow B=2.\left(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{15.16}\right)\)
\(\Rightarrow B=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(\Rightarrow B=2.\frac{3}{16}\)
\(\Rightarrow B=\frac{3}{8}\)
Vậy \(B=\frac{3}{8}\)
7 tháng 7 2016
C=220 +230 +242 +...+2240 =2×(120 +130 +142 +...+1240 )
C=2×(14×5 +15×6 +16×7 +...+115×16 )
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
\(B=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(B=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)
\(B=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(B=2\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(B=2.\frac{3}{16}=\frac{6}{16}=\frac{3}{8}\)
8 tháng 6 2015
À mình quên chỗ 1/5 phải là 1/15 nha bạn
Ta có:
\(C=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(C.\frac{1}{2}=\left(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\right).\frac{1}{2}\)
\(C.\frac{1}{2}=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\)
\(\frac{1}{2}C=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+..+\frac{1}{15.16}\)
\(\frac{1}{2}C=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\)
\(\frac{1}{2}C=\frac{1}{4}-\frac{1}{16}=\frac{3}{16}\)
\(\Rightarrow C=\frac{3}{8}\)
QD
27 tháng 5 2016
y = 1/10 + 1/15 + 1/21 + ... + 1/120
1/2y = 1/20 + 1/30 + 1/42 + ... + 1/240
1/2y = 1/4x5 + 1/5x6 + 1/6x7 + ... + 1/15x16
1/2y = 1/4 -1/5 + 1/5 - 1/6 + 1/6 -1/7 + ... +1/15 -1/16
1/2y = 1/4 - 1/16
1/2y = 3/16
y = 3/16 : 1/2
y = 3/16 x 2
y= 3/8
BN
27 tháng 5 2016
\(y=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(y=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(y=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)
\(y=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(y=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(y=2.\frac{3}{16}\)
\(y=\frac{3}{8}\)
Đặt A = \(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)
=> A = \(2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{240}\right)\)
= \(2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)
= \(2\left(\frac{1}{4}-\frac{1}{16}\right)=2\left(\frac{4}{16}-\frac{1}{16}\right)=2.\frac{3}{16}=\frac{3}{8}\)