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\(\frac{5}{2}+\frac{5}{4}+\frac{5}{8}+\frac{5}{16}+\frac{5}{32}+\frac{5}{64}+\frac{5}{128}+\frac{5}{256}\)
\(\Rightarrow5-\frac{5}{2}+\frac{5}{2}-\frac{5}{4}+\frac{5}{4}-\frac{5}{8}+\frac{5}{8}-\frac{5}{16}+...+\frac{5}{128}-\frac{5}{256}\)
\(\Rightarrow5-\frac{5}{256}\)
\(\Rightarrow\frac{1275}{256}\)
Ta có 5/2 + 5/4 + 5/8 + 5/16 + 5/32 + 5/64 + 5/128 + 5/256
= 5- 5/2 + 5/2 - 5/4 + 5/4 - 5/8 + 5/8 - 5/16 + 5/16 - 5/32 + 5/32 - 5/64 + 5/64 - 5/128 + 5/128 - 5/256
= 5-5/256
= 1275/256
tính bằng cách thuận tiện : \(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}...+\frac{1}{128}+\frac{1}{256}\)
Dễ lắm bạn à :
Đặt \(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{128}+\frac{1}{256}\)
\(\Rightarrow2A=2\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{128}+\frac{1}{256}\right)\)
\(\Leftrightarrow2A=2+1+\frac{1}{2}+\frac{1}{4}+....+\frac{1}{64}+\frac{1}{128}\)
\(\Leftrightarrow2A-A=2+1+\frac{1}{2}+\frac{1}{4}+....+\frac{1}{64}+\frac{1}{128}-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{128}+\frac{1}{256}\right)\)
\(\Leftrightarrow A=2-\frac{1}{256}=\frac{511}{256}\)
đặt A= 1+1/2+1/4+1/8+...+1/128+1/256
2A=2+1+1/2+1/4+...+1/64+1/128
2A-A=A=2-1/256=511/256
Bài làm
124 x 76 + 12 x 248
= 124 x 76 + 24 x 124
= 124 x ( 76 + 24 )
= 124 x 100
= 12400
Bài làm
128 x 68 + 16 x 256
= 128 x 68 + 32 x 128
= 128 x ( 68 + 32 )
= 128 x 100
b ) Đặt \(A=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{101.103}\)
\(\Rightarrow A=\frac{5}{2}\left(\frac{5}{1}-\frac{5}{3}+\frac{5}{3}-\frac{5}{5}+....+\frac{5}{101}-\frac{5}{103}\right)\)
\(\Rightarrow A=\frac{5}{2}\left(5-\frac{5}{103}\right)\)
1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
= 1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + ... + 1/256 - 1/512
= 1/2 - 1/512
= 255/512
Gọi \(\frac{1}{4}+\frac{1}{8}+\frac{1}{6}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\) là A
Ta có :
\(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)
\(2A=2.\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\right)\)
\(2A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(2A-A=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\right)-\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{11}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\right)\)
\(A=\frac{1}{2}-\frac{1}{512}\)
\(A=\frac{255}{512}\)
Vậy ..........
(64 x 64 +256 x 256)/ (256 x 256 + 1024 x 1024)
= (64 x 64 + 64 x4 x 64 x 4)/(256 x 256 + 256 x4 x 256 x4)
= [64 x 64(1+4 x4 )]/[256 x 256(1+ 4x4)]
=64 x 64 /256 x 256
= 64 x 64 / 64 x4 x 64 x4
= 1/16
\(\frac{\text{(64 x 64 +256 x 256)}}{\text{(256 x 256 + 1024 x 1024) }}\)
= \(\frac{\text{(64 x 64 + 64 x4 x 64 x 4)}}{\text{(256 x 256 + 256 x4 x 256 x4) }}\)
= \(\frac{\text{[64 x 64(1+4 x4 )]}}{\text{[256 x 256(1+ 4x4)] }}\)
=\(\frac{\text{64 x 64}}{\text{256 x 256 }}\)
= \(\frac{\text{ 64 x 64 }}{\text{64 x4 x 64 x4 }}\)
= \(\frac{1}{\text{16}}\)