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256 - 128 - 64 - 36 - 16 - 8 - 4 - 2 - 1
= (256 - 16) - (128 - 8) - (64 - 4) - (36 - 16) - (16 - 4 - 2) - 1
= 240 - 120 - 60 - 20 - 10 - 1
= 29
sửa tí
= (256 - 16) - (128 - 8) - (64 - 4) - (36 - 16) - 8 - 2 - 1
= 240 - 120 - 60 - 20 - 8 - 2 - 1
= -3
#)Giải :
\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+...+\frac{1}{256}-\frac{1}{512}\)
\(=\frac{1}{2}-\frac{1}{512}\)
\(=\frac{255}{512}\)
Lời giải
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+...+\frac{1}{256}-\frac{1}{512}\)
\(=\frac{1}{2}-\frac{1}{512}\)
\(=\frac{255}{512}\)
Có :
A = \(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(\Rightarrow2A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(\Rightarrow2A-A=\frac{1}{2}-\frac{1}{256}\)
\(A=\frac{128}{256}-\frac{1}{256}=\frac{127}{256}\)
Đặt \(A=\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(A=\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}+\frac{1}{2^8}\)
\(2A=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\)
\(2A-A=\left(\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\right)-\left(\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}+\frac{1}{2^8}\right)\)
\(A=\frac{1}{2^2}-\frac{1}{2^8}\)
\(A=\frac{1}{4}-\frac{1}{256}=\frac{63}{256}\)
\(\Rightarrow\frac{63}{256}.x=\frac{1}{512}=\frac{1}{2^9}\)
\(\Rightarrow\frac{63}{2^8}.x=\frac{1}{2^9}\)
\(\Rightarrow x=\frac{1}{2^9}:\frac{63}{2^8}=\frac{1}{2^9}.\frac{2^8}{63}=\frac{1}{2.63}=\frac{1}{126}\)
Ủng hộ mk nha !!! ^_^
Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
2A = 1/2 x 2 + 1/4 x 2 + 1/8 x 2 + 1/16 x 2 + 1/32 x 2 + 1/64 x 2 + 1/128 x 2 + 1/256 x 2 + 1/512 x 2
2A = 1 + 1/2 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
2A - A = ( 1 + 1/2 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 ) - ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 )
A = 1 - 1/512
A = 511/512
\(P=\dfrac{1}{256}+\dfrac{1}{128}+...+1\)
\(=1+\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+...+\left(\dfrac{1}{2}\right)^8\)
=>\(2P=2+1+\dfrac{1}{2}+...+\left(\dfrac{1}{2}\right)^7\)
=>\(2P-P=2+1+\dfrac{1}{2}+...+\left(\dfrac{1}{2}\right)^7-1-\dfrac{1}{2}-\left(\dfrac{1}{2}\right)^2-...-\left(\dfrac{1}{2}\right)^8\)
=>\(P=2-\left(\dfrac{1}{2}\right)^8=\dfrac{511}{256}\)