1/2+1/4+1/8+1/16+1/32+....+1/1024
1+1/2+1/4+1/8+1/16+1/32+......+1/1024
A = 1/2+1/4+1/8+1/16+1/32+...+1/1024
1/2+1/4+1/8+1/16+1/32+...+1/1024 = ?
A = 1/2-1/4+1/8-1/16+1/32-................-1/1024+1/2048
1+ 1/2 + 1/4 + 1/8 + 1/16+ 1/32 +1/64 + .... + 1/512 +1/1024
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1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+/1024
1-1/2-1/4-1/8-1/16-1/32-...-1/1024-1/2048
tính nhanh
Đặt \(A=1-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-..-\frac{1}{2048}\)
\(\Rightarrow A=1-\left(1-\frac{1}{2}\right)-\left(\frac{1}{2}-\frac{1}{4}\right)-..-\left(\frac{1}{1024}-\frac{1}{2048}\right)\)
\(\Rightarrow A=1-1+\frac{1}{2}-\frac{1}{2}+\frac{1}{4}-..-\frac{1}{1024}+\frac{1}{2018}\)
\(\Rightarrow A+\frac{1}{2018}\)
1-1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256-1/512-1/1024-1/2048 =0.00048828125
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024 =?
gọi A=1/2+1/4+1/8+...+1/1024
2xA=1+1/2+1/4+.....+1/512
2xA-A=(1+1/2+1/4+....+1/512)-(1/2+1/4+1/8+...+1/1024)
A=1-1/1024
=1023/1024
vậy A=1023/1024
\(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{1024}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+...+\frac{1}{512}-\frac{1}{1024}=1-\frac{1}{1024}=\frac{1023}{1024}\)
Đặt tổng trên là A. Ta có
A x 2 = 1+ 1/2+1/4+1/8+ 1/16+1/32+ 1/64+ 1/128 + 1/256 + 1/512
Ax2 - A = 1+ 1/2+1/4+1/8 +1/16 + 1/32 +1/64+ 1/128 + 1/256+ 1/512 - ( 1/2 + 1/4 +1/8+1/16+1/32+1/64 + 1/128+ 1/256 + 1/512+ 1/1024)
A = 1+ 1/2 +1/4+1/8+1/16+1/32+1/64+1/128+1/256 + 1/512 - 1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256-1/512- 1/1024
A = 1 - 1/ 1024 = 1023/1024
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
đặt biểu thức là A ta có :
A = 1/2 + 1/4 + 1/8 + 1/16 +1/32 +1/64 +1/128 + 1/256 + 1/512 + 1/102
A x 2 = 1+ 1/2 + 1/4 + 1/8 + 1/16 +1 /32+1/64 + 1/ 128 + 1/256 + 1/512
A = ( 1 + 1/2 +1/4 + 1/ 8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 ) - ( 1/2 + 1/4 + 1/8 +1/16 +1/32 + 1/64 + 1/128 +1/256 +1/512 +1/1024)
A = 1 - 1/1024
A = 1023/1024
nhớ k nhé
(1 / 2) + (1 / 4) + (1 / 8) + (1 / 16) + (1 / 32) + (1 / 64) + (1 / 128) + (1 / 256) + (1 / 512) + (1 / 1024) =
0.9990234375
A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024
a*2=1+1/2+1/4+1/8+1/16+...+1/512
a*2-a=1+1/2+1/4+...+1/512-1/2-1/4-1/8-/...-1/1024
a=1-1/1204
a=1023/1024