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tính nhanh
49/5-1/2-1/4-1/8-1/16-1/32=8,83125
nha bn duyệt đi
\(\frac{49}{5}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}=\frac{1413}{160}=8,83125\)
Ta có : \(\frac{49}{5}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}\)
\(=\frac{49}{5}-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
=> \(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
=> \(2A-A=1-\frac{1}{32}\Rightarrow A=\frac{31}{32}\)
Vậy \(\frac{49}{5}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}\)
\(=\frac{49}{5}-\frac{31}{32}=\frac{1413}{160}\)
\(\frac{49}{5}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}\)\(=\)\(\frac{4189}{480}\)
a. \(\dfrac{17}{13}-\dfrac{14}{23}+\dfrac{9}{13}-\dfrac{9}{23}=\left(\dfrac{17}{13}+\dfrac{9}{13}\right)-\left(\dfrac{14}{23}+\dfrac{9}{23}\right)=\dfrac{26}{13}-\dfrac{23}{23}=2-1=1\)
b.\(\dfrac{49}{5}-\dfrac{1}{2}-\dfrac{1}{4}-\dfrac{1}{32}-\dfrac{1}{16}-\dfrac{1}{32}=\dfrac{49}{5}-\left(1-\dfrac{1}{32}\right)=\dfrac{44}{5}+\dfrac{1}{32}=\dfrac{1413}{160}\)
Đặt A=1/2+1/4+1/8+1/16+1/32
2A=1+1/2+1/4+1/8+1/16
Ta có:
2A-A=1+1/2+1/4+1/8+1/16-(1/2+1/4+1/8+1/16+1/32)
A=1-1/32=31/32
Ta đặt :
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(A\cdot2=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\cdot2\)
\(A\cdot2=\frac{1}{2}\cdot2+\frac{1}{4}\cdot2+\frac{1}{8}\cdot2+\frac{1}{16}\cdot2+\frac{1}{32}\cdot2\)
\(A\cdot2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(A\cdot2-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
\(A=1-\frac{1}{32}\)
\(A=\frac{31}{32}\)
Lời giải:
$\frac{49}{5}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{32}$
$=\frac{49}{5}-\frac{16}{32}-\frac{8}{32}-\frac{4}{32}-\frac{1}{32}$
$=\frac{49}{5}-\frac{29}{32}=\frac{1423}{160}$
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(A=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}\)
\(2A-A=1-\frac{1}{2^5}\)
\(A=\frac{32}{32}-\frac{1}{32}\)
\(A=\frac{31}{32}\)
49/5 + 1/2 - 1/4 - 1/8 - 1/16 - 1/32 = 1413/60 = 8,83125
1573/160 tính mệt ghê