1/2-1/8-1/16-1/32-1/64-1/128=
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X x (1/2+1/4+1/8+1/16+1/32+1/64+1/128) = 127/128
X x 127/128 = 127/128
X = 127/128 : 127/128
X = 1
1+1=2
2+2=4
4+4=8
8+8=16
16+16=32
32+32=64
64+64=128
128+128=256
b: A=1/3+1/9+...+1/3^10
=>3A=1+1/3+...+1/3^9
=>A*2=1-1/3^10=(3^10-1)/3^10
=>A=(3^10-1)/(2*3^10)
c: C=3/2+3/8+3/32+3/128+3/512
=>4C=6+3/2+...+3/128
=>3C=6-3/512
=>C=1023/512
d: A=1/2+...+1/256
=>2A=1+1/2+...+1/128
=>A=1-1/256=255/256
C= \(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}\)
2C = \(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\)
2C-C = \(1-\dfrac{1}{128}\)
C= \(\dfrac{127}{128}\)
Đặt A=\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2A-A=1-\frac{1}{128}\)
\(A=\frac{127}{128}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}=\frac{127}{128}\)
1/2+1/4+1/8+1/16+1/32+1/64+1/128
=1/1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128
=1/1-1/128
=127/128
kq = \(\frac{127}{128}\)Bạn chỉ cần bấm máy tính là ra bài này dễ mà hihi :D :))
Gọi biểu thức trên là A ta có
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
=> \(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
=> \(A=2A-A\)\(=1-\frac{1}{128}\)
Vậy \(A=1-\frac{1}{128}\)
ctv olm có mặt ạ
A = \(\dfrac{1}{2}\) - \(\dfrac{1}{8}\) - \(\dfrac{1}{16}\) - \(\dfrac{1}{32}\) - \(\dfrac{1}{64}\) - \(\dfrac{1}{128}\)
2x A = 1 - \(\dfrac{1}{4}\)- \(\dfrac{1}{8}\) - \(\dfrac{1}{16}\) - \(\dfrac{1}{32}\) - \(\dfrac{1}{64}\)
2A - A = 1 - \(\dfrac{1}{4}\) - \(\dfrac{1}{2}\) +\(\dfrac{1}{128}\)
A = \(\dfrac{33}{128}\)
1/2-1/8-1/16-1/32-1/64-1/128
= 64/128 - 16/128 - 8/128 - 4/128 - 2/128 - 1/128
= 64-16-8-4-2-1 / 128
= 33/128