tinh nhanh :
1/2+1/4+1/8+1/16+1/32=
K
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19 tháng 8 2015
A x 2 = 1 + 1/2+1/4+1/8+1/16+1/32
A x 2 - A = (1 + 1/2+1/4+1/8+1/16+1/32 ) - ( 1/2+1/4+1/8+1/16+1/32 +1/64)
A = 1 - 1/64
A = 63/64
DD
Đoàn Đức Hà
Giáo viên
3 tháng 6 2021
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(2\times A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2\times A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)\)
\(A=1-\frac{1}{128}\)
\(A=\frac{127}{128}\)
DD
Đoàn Đức Hà
Giáo viên
3 tháng 6 2021
\(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(2\times B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\)
\(B=1-\frac{1}{16}=\frac{15}{16}\)
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(\Leftrightarrow4\times x+\frac{15}{16}=1\)
\(\Leftrightarrow4\times x=\frac{1}{16}\)
\(\Leftrightarrow x=\frac{1}{64}\)
T
16 tháng 6 2019
#)Giải :
\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{1}{64}+\frac{1}{64}-\frac{1}{128}\)
\(=\frac{1}{2}-\frac{1}{128}\)
\(=\frac{63}{128}\)
MT
4
1 tháng 7 2015
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
HT
15 tháng 7 2015
A=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)
A=\(\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+...+\left(\frac{1}{128}-\frac{1}{256}\right)\)
A=\(1-\frac{1}{256}\)
A=\(\frac{255}{256}\)
C
13 tháng 8 2018
A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
2A = 1/2 x 2 + 1/4 x 2 + 1/8 x 2 + 1/16 x 2 +1/32 x 2 + 1/64 x 1/128 + 1/256 x 2
2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
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 )
A = 1 - 1/256
A = 255/256
10 tháng 8 2016
1.a
1/2+1/4+1/8+1/16+1/32
= 1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32
= 1-1/32=31/32
10 tháng 8 2016
1b
\(\frac{1}{2}.\frac{1}{2}+\frac{1}{2}.\frac{1}{3} +\frac{1}{3}+\frac{1}{3}+\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{6}+\frac{2}{3}+\frac{1}{4}+\frac{1}{20}+\frac{1}{30}\)
\(=\frac{5}{20}+\frac{5}{30}+\frac{20}{30}+\frac{5}{20}+\frac{1}{20}+\frac{1}{30}\)
\(=\left(\frac{5}{20}+\frac{5}{20}+\frac{1}{20}\right)+\left(\frac{5}{30}+\frac{20}{30}+\frac{1}{30}\right)\)
\(=\frac{11}{20}+\frac{26}{30}\)
\(=\frac{11}{20}+\frac{13}{15}\)
\(=\frac{17}{12}\)
12 tháng 4 2015
ta có:A=1/2+1/2^2+1/2^3+...+1/2^6+1/2^7 (1)
2A= 2.(1/2+1/2^2+1/2^3+...+1/2^6+1/2^7)
=1+1/2+1/2^2+....+1/2^6+1/2^7 (2)
lấy (2) trừ (1) vế với vế ta được:
2A-A=(1+1/2+1/2^2+....+1/2^6+1/2^7)-(1/2+1/2^2+...+1/2^6+1/2^7)
A=1-1/2^7
VẬY A=1-1/2^7
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=\frac{16}{32}+\frac{8}{32}+\frac{4}{32}+\frac{2}{32}+\frac{1}{32}\)
=\(\frac{16+8+4+2+1}{32}=\frac{31}{32}\)