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2
8 tháng 5 2015
A=\(2.\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+......+\frac{1}{240}\right)\)
A=\(2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)
A=\(2.\left(\frac{1}{4.}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.......+\frac{1}{15}-\frac{1}{16}\right)\)
A=\(2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
A=\(2.\left(\frac{4}{16}-\frac{1}{16}\right)\)
\(A=2.\frac{3}{16}\)
\(A=\frac{3}{8}\)
\(Vay\) \(A=\frac{3}{8}\)
KT
9 tháng 8 2018
\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{105}+\frac{1}{210}\)
=> \(\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+.....+\frac{1}{210}+\frac{1}{240}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{14.15}+\frac{1}{15.16}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{!}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{16}\)
\(=\frac{1}{2}-\frac{1}{16}=\frac{7}{16}\)
=> \(A=\frac{7}{8}\)
TT
3
S
15 tháng 5 2023
\(A=\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+...+\dfrac{1}{120}\)
\(=2\left(\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+...+\dfrac{1}{240}\right)\)
\(=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{15.16}\right)\)
\(=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)
\(=2\left(\dfrac{1}{4}-\dfrac{1}{16}\right)\)
\(=2\cdot\dfrac{3}{16}\)
\(=\dfrac{3}{8}\)
\(A:x=759\)
\(\dfrac{3}{8}:x=759\)
\(\Rightarrow x=\dfrac{3}{8}:759=\dfrac{1}{2024}\)
#AvoidMe
15 tháng 5 2023
A=2(1/20+1/30+...+1/240)
=2(1/4-1/5+1/5-1/6+...+1/15-1/16)
=2*3/16=3/8
A:x=759
=>x=3/8:759=1/2024
14 tháng 4 2017
A = 1/10 + 1/15 + 1/21 + ....+ 1/120
= 2/20 + 2/30 + 2/42 +....+ 2/240
= 2/4x5 + 2/5x6 + 2/6x7 + ...+ 2/15x16
= 2 x ( 1/4x5 + 1/5x6 + 1/6x7 +...+ 1/15x16)
=2 x ( 1/4 - 1/5 + 1/5 - 1/6 +1/6 - 1/7 + .....+ 1/15 - 1/16 )
= 2 x ( 1/4 - 1/16 )
= 2 x ( 4/16 - 1/16 )
= 2 x 3/16
= 6/16
= 3/8
tk nhé
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
D
2 tháng 5 2015
Đặt A = \(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)
=> A = \(2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{240}\right)\)
= \(2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)
= \(2\left(\frac{1}{4}-\frac{1}{16}\right)=2\left(\frac{4}{16}-\frac{1}{16}\right)=2.\frac{3}{16}=\frac{3}{8}\)
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 )