so sánh: 1/2 - 1/4 - 1/8 - 1/16- 1/32 - 1/64 - 1/128
so vs 1
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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
G
1
DD
Đoàn Đức Hà
Giáo viên
22 tháng 6 2021
\(12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{32}-1\right)\left(5^{32}+1\right)\)
\(=\frac{1}{2}\left(5^{64}-1\right)\)
NT
23 tháng 6 2021
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
tính nhanh p/s 1+ 5/4 + 5/8 + 5/16 + 5/32 + 5/64
9 tháng 5 2023
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
\(\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}-\frac{1}{64}-\frac{1}{128}\)
\(=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)-2\times\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)\)
\(=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}-\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-\frac{1}{32}-\frac{1}{64}\)
\(=\frac{1}{128}\)< 1
còn 1 cách nữa mk lm nhưng ko chắc nên hỏi
1/2-(1/4+1/8+1/32+1/64+1/128)
=1/2-(1/2-1/4+1/4-1/8+1/8-1/32+1/32-1/64+1/64-1/128)
=1/2-(1/2-1/128)
=1/2-63/128
=1/128