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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
\(ĐặtA=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\)
\(A=1-\frac{1}{64}=\frac{63}{64}\)
Đặt :
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(\Leftrightarrow\)\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\)
\(\Leftrightarrow\)\(2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}\)
\(\Leftrightarrow\)\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^6}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^7}\right)\)
\(\Leftrightarrow\)\(A=1-\frac{1}{2^7}\)
Vậy \(A=1-\frac{1}{2^7}\)
a)
\(A=2+4+8+...+2048\)
\(A=2+2^2+...+2^{11}\)
\(2A=2^2+2^3+...+2^{12}\)
\(2A-A=\left(2^2+2^3+...+2^{12}\right)-\left(2+2^2+...+2^{11}\right)\)
\(A=2^{12}-2\)
a) 2+4+8+16+32+64+128+512+1024+2048
b thì minh cha ra. Mình sẽ cố làm ra b mong ban thong cam va bạn nho k đung cho minh nha
\(1\frac{1}{2}x1\frac{1}{3}:1\frac{1}{4}:1\frac{1}{5}\)
\(=\frac{3}{2}x\frac{4}{3}:\frac{5}{4}:\frac{6}{5}\)
\(=\frac{3}{2}x\frac{4}{3}x\frac{4}{5}x\frac{5}{6}\)
\(=\frac{4x4}{2x6}=\frac{2x2x4}{2x2x3}=\frac{4}{3}\)
\(1\frac{1}{2}\times1\frac{1}{3}\div1\frac{1}{4}\div1\frac{1}{5}=\frac{3}{2}\times\frac{4}{3}\div\frac{5}{4}\div\frac{6}{5}=\frac{3}{2}\times\frac{4}{3}\times\frac{4}{5}\times\frac{5}{6}\)
\(=\frac{3\times4\times4\times5}{2\times3\times5\times6}=\frac{4}{3}\)
(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
\(\frac{\text{(64 x 64 +256 x 256)}}{\text{(256 x 256 + 1024 x 1024) }}\)
= \(\frac{\text{(64 x 64 + 64 x4 x 64 x 4)}}{\text{(256 x 256 + 256 x4 x 256 x4) }}\)
= \(\frac{\text{[64 x 64(1+4 x4 )]}}{\text{[256 x 256(1+ 4x4)] }}\)
=\(\frac{\text{64 x 64}}{\text{256 x 256 }}\)
= \(\frac{\text{ 64 x 64 }}{\text{64 x4 x 64 x4 }}\)
= \(\frac{1}{\text{16}}\)