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a) Đặt A= 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
2A= 2(1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)
= 1+1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
=>A = 2A-A =1+1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 -1/2 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64 - 1/128 - 1/256
=1-1/256
=255/256
b) = 18 - (19/21 + 8/9) = 18 - 113/63 = 1021/63
\(\dfrac{2006\times2005-1}{2004\times2006+2005}=\dfrac{2006\times\left(2004+1\right)-1}{2004\times2006+2005}\)
\(=\dfrac{2004\times2006+2006-1}{2004\times2006+2005}=\dfrac{2004\times2006+2005}{2004\times2006+2005}\)
\(=1\)
\(18\times\left(\dfrac{19191919+88888}{21212121+99999}\right)=18\times\left(\dfrac{19}{21}+\dfrac{8}{9}\right)\)
\(=18\times\dfrac{113}{63}=\dfrac{226}{7}=32\dfrac{2}{7}\)
\(\frac{63.\left(19191919+88888\right)}{212121+99999}=\frac{63.\left(19191919+18181+70707\right)}{21212121+97979+2020}=\frac{63.\left(19200000+70707\right)}{21300000+2020}\)\(=\frac{63.19270707}{21302020}\)
\(18.\left(\frac{19191919}{21212121}+\frac{88888}{99999}\right)=18.\left(\frac{19}{21}+\frac{8}{9}\right)=18.\frac{113}{63}=\frac{226}{7}nha!!!!!\)
\(\frac{226}{7}\)