Tính 1/8 + 1/24 +1/48 +1/120+ 1/168 + 1/224 + 1/288 + 1/360
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Tính 1/8 + 1/24 +1/48 +1/120+ 1/168 + 1/224 + 1/288 + 1/360
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Những câu hỏi liên quan
26 tháng 4 2019
A=1/8+1/24+1/48+1/80+1/120+1/168+1/224=>2A=2/8+2/24+2/48+2/80+2/120+2/168+2/224
2A=2/2*4+2/4*6+2/6*8+2/8*10+2/10*12+2/12*14+2/14*16
2A=1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12+1/12-1/14+1/14-1/16
2A=1/2-1/16
2A=7/16
A=7/16:2
A=7/32
21 tháng 3 2023
=\(1+\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+...+\dfrac{1}{10\cdot12}\)
\(=1+\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{10}-\dfrac{1}{12}\right)\)
\(=1+\dfrac{1}{2}\cdot\dfrac{5}{12}=1+\dfrac{5}{24}=\dfrac{29}{24}\)
21 tháng 3 2023
=1+12⋅4+14⋅6+...+110⋅121+12⋅4+14⋅6+...+110⋅12
=1+12(12−14+14−16+...+110−112)=1+12(12−14+14−16+...+110−112)
=1+12⋅512=1+524=2924
BC
2
19 tháng 7 2016
\(\frac{1}{4}+\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120}+\frac{1}{168}\)
\(=\frac{1}{4}.\left(1+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(=\frac{1}{4}.\left(1+\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(=\frac{1}{4}.\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(=\frac{1}{4}.\left(1+1-\frac{1}{7}\right)\)
\(=\frac{1}{4}.\left(2-\frac{1}{7}\right)\)
\(=\frac{1}{4}.\frac{13}{7}=\frac{13}{28}\)
VA
19 tháng 7 2016
Ta có :
Đặt \(A=\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120}+\frac{1}{168}\)
\(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\)
\(2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}+\frac{2}{12.14}\)
\(2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\)
\(2A=\frac{1}{2}-\frac{1}{14}\)
\(2A=\frac{7}{14}-\frac{1}{14}=\frac{3}{7}\)
\(A=\frac{3}{7}:2=\frac{3}{14}\)
=> \(\frac{1}{4}+\frac{3}{14}=\frac{7}{28}+\frac{6}{28}=\frac{13}{28}\)
Ủng hộ mk nha !!! ^_^
LT
Lương Thị Vân Anh
CTVHS
2 tháng 3 2023
\(A=1+\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)
\(=1+\dfrac{1}{2\times4}+\dfrac{1}{4\times6}+\dfrac{1}{6\times8}+\dfrac{1}{8\times10}+\dfrac{1}{10\times12}\)
\(=1+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{12}\)
\(=1+\dfrac{1}{2}-\dfrac{1}{12}=\dfrac{17}{12}\)
28 tháng 2 2018
A = 1 + 1/2.4 + 1/4.6 + 1/6.8 + 1/8.10 + 1/10.12
2A = 2 + 2/2.4 + 2/4.6 + 2/6.8 + 2/8.10 + 2/10.12
= 2 + 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + 1/8 - 1/10 + 1/10 - 1/12
= 2 + 1/2 - 1/12 = 29/12
=> A = 29/12 : 2 = 29/24
Tk mk nha
TD
1
5 tháng 4 2021
Ta có: \(A=1+\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)
\(\Leftrightarrow2A=2+\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+\dfrac{2}{8\cdot10}+\dfrac{2}{10\cdot12}\)
\(\Leftrightarrow2A=2+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{12}\)
\(\Leftrightarrow2A=2+\dfrac{1}{2}-\dfrac{1}{12}\)
\(\Leftrightarrow2A=\dfrac{24}{12}+\dfrac{6}{12}-\dfrac{1}{12}\)
\(\Leftrightarrow2A=\dfrac{29}{12}\)
hay \(A=\dfrac{29}{24}\)
TP
4
12 tháng 4 2016
\(\frac{1}{6}:\frac{1}{7}:\frac{1}{8}\)
=\(\frac{1}{6}x\frac{1}{7}:\frac{1}{8}\)
=\(\frac{1}{42}:\frac{1}{8}\)
=\(\frac{1}{42}x\frac{8}{1}\)
=\(\frac{8}{42}\)=\(\frac{4}{21}\)
\(\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{120}+\dfrac{1}{168}+\dfrac{1}{224}+\dfrac{1}{288}+\dfrac{1}{360}\)
\(=\dfrac{1}{2\text{x}4}+\dfrac{1}{4\text{x}6}+...+\dfrac{1}{18\text{x}20}\)
\(=\dfrac{1}{2}\text{x}\left(\dfrac{2}{2\text{x}4}+\dfrac{2}{4\text{x}6}+...+\dfrac{2}{18\text{x}20}\right)\)
\(=\dfrac{1}{2}\text{x}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{18}-\dfrac{1}{20}\right)\)
\(=\dfrac{1}{2}\text{x}\left(\dfrac{1}{2}-\dfrac{1}{20}\right)=\dfrac{1}{2}\text{x}\dfrac{9}{20}=\dfrac{9}{40}\)
81+241+481+1201+1681+2241+2881+3601
=12x4+14x6+...+118x20=2x41+4x61+...+18x201
=12x(22x4+24x6+...+218x20)=21x(2x42+4x62+...+18x202)
=12x(12−14+14−16+...+118−120)=21x(21−41+41−61+...+181−201)
=12x(12−120)=12x920=940=21x(21−201)=21x209=409