Cho B=3/2+3/4+3/8+3/16+3/32+3/64+3/128
Tìm B
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NT
3
18 tháng 8 2018
b:3=1/2+1/4+1/8+1/16+1/32+1/64+1/128
[b:3]x2=1+1/2+1/4+1/8+1/16+1/32+1/64
[b:3]x2-[b:3]=1+1/2+1/4+1/8+1/16+1/32+1/64-1/2+1/4+1/8+1/16+1/32+1/64+1/128
b:3=1-1/128
b:3=127/128
b=127/128x3
b=381/128
18 tháng 8 2018
B.2=\(3+\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}\)\(+\frac{3}{128}\)
B.2-B=\(\left(3+\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}+\frac{3}{128}\right)\).\(\left(\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}+\frac{3}{128}\right)\)
B=3-\(\frac{3}{128}\)
B=\(\frac{381}{128}\)
NM
0
TL
2
NT
Chứng minh rằng:
a) 1/2-1/4+1/8-1/16+1/32-1/64<1/3
b) 1/3-2/3^2+3/3^3-3/3^4+...+99/3^99-100/3^100<3/16
0
26 tháng 6 2022
a: \(=3\cdot\left(\dfrac{1}{4}-\dfrac{6}{7}+\dfrac{8}{21}\right)\)
\(=3\cdot\left(\dfrac{21}{84}-\dfrac{72}{84}+\dfrac{32}{84}\right)\)
\(=\dfrac{-19}{28}\)
b: \(=\dfrac{-2}{3}\left(\dfrac{1}{9}-\dfrac{1}{6}-\dfrac{1}{11}\right)\)
\(=\dfrac{-2}{3}\cdot\dfrac{-29}{198}=\dfrac{29}{99\cdot3}=\dfrac{29}{297}\)
c: \(=\dfrac{-3}{7}+\dfrac{4}{25}+\dfrac{5}{16}+\dfrac{3}{16}\)
\(=\dfrac{-75+28}{175}+\dfrac{1}{2}\)
\(=\dfrac{-47}{175}+\dfrac{1}{2}=\dfrac{-94+175}{350}=\dfrac{81}{350}\)
d: \(=\dfrac{-4}{9}\cdot\left(\dfrac{1}{26}-\dfrac{1}{2}-\dfrac{1}{8}\right)\)
\(=\dfrac{-4}{9}\cdot\dfrac{-61}{104}=\dfrac{61}{26\cdot9}=\dfrac{61}{234}\)
b:3=1/2+1/4+1/8+1/16+1/32+1/64+1/128
[b:3]x2=1+1/2+1/4+1/8+1/16+1/32+1/64
[b:3]x2-[b:3]=1+1/2+1/4+1/8+1/16+1/32+1/64-1/2+1/4+1/8+1/16+1/32+1/64+1/128
b:3=1-1/128
b:3=127/128
b=127/128x3
b=381/128
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