tính
A=2/20+2/30+2/42+...+2/240
(dấu / này là dấu phần)
K
Khách
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18 tháng 3 2019
A=1/6+1/12+1/20+1/30+1/42+1/56+1/72
A=1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9
A=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
A=1/2-1/9
Câu B tương tự nha bạn :333
13 tháng 12 2021
\(a,3^3+3^2-\left(2^7:2^5+7^8:7^7\right)=27+9-\left(2^2+7\right)=36-11=25\)
\(b,27.77+27.27-27=27\left(77+27-1\right)=27.103=2781\)
\(c,52:\left(43-30\right)+144-16=52:13+128=4+128=132\)
\(f,3^2.101-3^2.101^0=3^2\left(101-101^0\right)=9\left(101-1\right)=9.100=900\)
BD
1 tháng 10 2017
131 . x - 942 = 2^7 . 2^3
131 . x - 942 = 2^10
131 . x - 942 = 1024
131 . x = 1024 + 942
131 . x = 1966
x = 1966 : 131
x \(\approx15\)
b ) [ ( x + 32 ) - 17 ] . 2 = 42
[ ( x + 32 ) - 17 ] = 42 : 2
( x + 32 ) - 17 = 21
x + 32 = 21 + 17
x + 32 = 38
x = 38 - 32
x = 6
16 tháng 8 2018
a)\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+x=\frac{3}{5}\)
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+x=\frac{3}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}+x=\frac{3}{5}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{10}+x=\frac{3}{5}\)
\(\Rightarrow\frac{2}{5}+x=\frac{3}{5}\)
\(\Rightarrow x=\frac{3}{5}-\frac{2}{5}=\frac{1}{5}\)
b)\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}+x=\frac{1}{3}\)
\(\Rightarrow\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+...+\frac{2}{13}-\frac{2}{15}+x=\frac{1}{3}\)
\(\Rightarrow\frac{2}{3}-\frac{2}{15}+x=\frac{1}{3}\)
\(\Rightarrow\frac{8}{15}+x=\frac{1}{3}\)
\(\Rightarrow x=\frac{1}{3}-\frac{8}{15}=-\frac{1}{5}\)
c)\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{9}{10}\)
\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{9}{10}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{9}{10}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{x+1}=\frac{9}{10}\)
\(\Leftrightarrow\frac{x+1-1}{x+1}=\frac{9}{10}\)
\(\Rightarrow\frac{x}{x+1}=\frac{9}{10}\)
\(\Rightarrow x=9\)
DD
Đoàn Đức Hà
Giáo viên
10 tháng 1 2021
b) \(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}+x=\frac{1}{3}\)
\(\Leftrightarrow\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{15-13}{13.15}+x=\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}+x=\frac{1}{3}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{15}+x=\frac{1}{3}\)
\(\Leftrightarrow x=\frac{1}{15}\)
MC
25 tháng 7 2018
\(a)A=\dfrac{2}{20}+\dfrac{2}{30}+\dfrac{2}{42}+...+\dfrac{2}{240}\)
\(A=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{15.16}\right)\)
\(A=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)
\(A=2\left(\dfrac{4}{16}-\dfrac{1}{16}\right)\)
\(A=\dfrac{2.3}{16}\)
\(=\dfrac{3}{8}\)
\(b)B=\dfrac{5}{6}+\dfrac{11}{12}+\dfrac{19}{20}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}\)
\(B=\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+...+\left(1-\dfrac{1}{56}\right)\)
\(B=6-\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{7.8}\right)\)
\(B=6-\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}\right)\)
\(B=6-\left(\dfrac{4}{8}-\dfrac{1}{8}\right)\)
\(B=\dfrac{48}{8}-\dfrac{3}{8}\)
\(B=\dfrac{45}{8}\)
DA
4
21 tháng 4 2016
\(A=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(A=2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(A=2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)
\(A=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(A=2.\frac{3}{16}\)
\(A=\frac{3}{8}\)
21 tháng 4 2016
A=2/20+2/30+2/42+...+2/240
=>A/2=1/20+1/30+1/42+...+1/240
=>A/2=1/(4*5)+1/(5*6)+1/(6*7)+...+1/(15*16)
=>A/2=1/4-1/5+1/5-1/5+1/6-1/7+...+1/15-1/16
=>A/2=1/4-1/16
=>A/2=3/16
=>A=3/8
G
1
3 tháng 1
`#3107.101107`
\(\left(\dfrac{2}{3}\right)^x+\left(\dfrac{2}{3}\right)^{x+2}=\dfrac{104}{243}?\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x+\left(\dfrac{2}{3}\right)^x\cdot\left(\dfrac{2}{3}\right)^2=\dfrac{104}{243}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x\cdot\left(1+\dfrac{2^2}{3^2}\right)=\dfrac{104}{243}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x\cdot\left(1+\dfrac{4}{9}\right)=\dfrac{104}{243}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x\cdot\dfrac{13}{9}=\dfrac{104}{243}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\dfrac{104}{243}\div\dfrac{13}{9}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\dfrac{8}{27}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\dfrac{2^3}{3^3}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^3\)
\(\Rightarrow x=3\)
Vậy, `x = 3.`
Quy luật là :
20=4x5;30=5x6;42=6x7......240=15x16
Còn lại mình không biết . Để mình coi
\(A=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)
\(=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(=2\left(\frac{1}{4}-\frac{1}{16}\right)=2\left(\frac{4-1}{16}\right)=2.\frac{3}{16}=\frac{3}{8}\)