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1/2 + 1/4 + 1/8 + 1/16 + ... + 1/256 + 1/512
= 256/512 + 128/512 + 64/512 + ... + 2/512 + 1/512
= 256 + 128 + 64 + .. + 2 + 1 / 512
= ???????
s=1/2+1/4+1/8+1/16+.....+1/256+1/512
sx2=(1/2+1/4+1/8+1/16+....+1/256+1/512)x2
sx2=1+1/2+1/4+1/8+......+1/126+1/256
sx2-s=(1+1/2+1/4+1/8+......+1/256)-(1/2+1/4+1/8+1/16++.....+1/256+1/512)
1+1/2+1/4+1/8+......+1/256-1/2-1/4-1/8-1/16-.....1/256-1/512
=1-1/512=511/512
Ta có: A =1/2+1/4+1/8+1/16+....+1/256+1/512
=> 2A = 1 + 1/2 + 1/4 + 1/8 + ...+ 1/128 + 1/256
=> 2A - A = (1 + 1/2 + 1/4 + 1/8 + ...+ 1/128 + 1/256 -(1/2+1/4+1/8+1/16+....+1/256+1/512 )
A = 1 - 1/512 = 511/512
Đặt A=1/2+1/4+1/8+..+1/1024
Ax2=1+1/2+1/4+1/8+..+1/512( Nhân cả 2 vế với 2)
Ax2-A=(1+1/2+1/4+1/8+..+1/512)-(1/2+1/4+1/8+..+1/1024)
<=>A=1-1/1024
<=>A=1023/1024
Vậy biểu thức đã cho = 1023/1024
1/2=1/1-1/2
1/4=1/2-1/4
1/8=1/4-1/8
...................
1/1024=1/512-1/1024
Đặt biểu thức=A
A=1/1-1/2+1/2-1/4+1/4-1/8+........+1/512-1/1024
A=1/1-1/1024
A=1023/1024
bạn thấy cách của mik có dễ hiểu ko,nếu dễ hiểu thì k nha
có cách khác : 1/2+ 1/4= 3/4
1/2+ 1/4 +1/8 = 7/8
vậy :1/2+ 1/4 +1/8 + ....+ 1/1024 =1023/1024
A = 1/2 + 1/4 + 1/8 + ... + 1/1024
2A = 1 + 1/2 + 1/4 + ... + 1/512
2A - A = (1 + 1/2 + 1/4 + ... + 1/512) - (1/2 + 1/4 + 1/8 + ... + 1/1024)
A = 1 - 1/1024
A = 1023/1024
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{1024}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+......+\frac{1}{512}\)
\(\Rightarrow A=2A-A=1-\frac{1}{1024}\)
\(A=\frac{1023}{1024}\)
đặt tên là A
ta có :
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+..\frac{1}{512}\)
\(2A=2.\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{512}\right)\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{512}\right)\)
\(A=1-\frac{1}{512}\)
\(A=\frac{511}{512}\)
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