tính nhanh D = 2/3 + 2/6 + 2/12 +2/24 +.... + 2/768
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B1 :
a, = -2-2-2= -6
b, = -2-2-2 = -6
B2:a, = 768-39-768 = (768-768)-39=0-39=-39
b, = -1579-12+1579 = (-1579+1579)-12 = 0-12=-12
k mk nha
=\(2.\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{98}+\frac{1}{192}\right)\)
=2.\(\frac{6272+3136+1568+784+392+192+98}{18816}\)
=24884/18816
=1,32
\(2\times169\times12-3\times68\times8-24\)
\(=24\times169-24\times68-24\)
\(=24\times\left(169-68-1\right)\)
\(=24\times100=2400\)
Đặt \(A=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}+\frac{2}{192}\)
\(\frac{1}{2}A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)
\(\frac{1}{4}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}\)
\(\frac{1}{2}A-\frac{1}{4}A=\frac{1}{3}-\frac{1}{384}\)
\(\frac{1}{4}A=\frac{127}{384}\)
\(A=\frac{127}{384}.4=\frac{127}{96}\)
2/3+2/6+2/12+2/24+2/48+2/96+2/192
=2/3+1/3+1/6+1/12+1/24+1/48+1/96
=\(\frac{64+32+16+8+4+2+1}{96}=\frac{127}{96}\)
a: \(\left(\frac45-\frac{13}{20}\right):\frac35\)
\(=\left(\frac{16}{20}-\frac{13}{20}\right)\cdot\frac53\)
\(=\frac{3}{20}\cdot\frac53=\frac{5}{20}=\frac14\)
b: \(197-13\cdot8+768\)
=197-104+768
=93+768
=861
c: \(20,7+1,47:7-23\%\cdot5\)
=20,7+0,21-1,15
=19,76
d: \(\frac{21}{77}\cdot\frac12+\frac{4}{11}\cdot\frac16+\frac{5}{11}\cdot\frac13\)
\(=\frac{3}{11}\cdot\frac12+\frac{2}{11}\cdot\frac13+\frac{5}{11}\cdot\frac13=\frac{3}{11}\cdot\frac12+\frac{7}{11}\cdot\frac13=\frac{3}{22}+\frac{7}{33}\)
\(=\frac{9}{66}+\frac{14}{66}=\frac{23}{66}\)
\(\dfrac{3}{2}xD=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\)
Đặt
\(A=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}\)
\(2xA=2+1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}\)
\(A=2xA-A=2-\dfrac{1}{256}=\dfrac{511}{256}=\dfrac{3}{2}xD\)
\(\Rightarrow D=\dfrac{511}{256}:\dfrac{3}{2}\)