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Ta có : \(A=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^7}+\frac{1}{2^8}\)
\(\Rightarrow2A=1+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^6}+\frac{1}{2^7}\)
\(\Rightarrow2A-A=\left(1+\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^6}+\frac{1}{2^7}\right)-\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^7}+\frac{1}{2^8}\right)\)
\(\Rightarrow A=1-\frac{2}{8}=\frac{256}{256}-\frac{1}{256}=\frac{255}{256}\)
\(a,\frac{8}{9}-\frac{1}{3}\div\frac{1}{2}\)
\(=\frac{8}{9}-\frac{1}{3}\times\frac{1}{2}\)
\(=\frac{8}{9}-\frac{1}{6}\)
\(=\frac{13}{18}\)
\(b,\left(\frac{3}{10}+\frac{4}{5}\times\frac{1}{2}\right)\div\left(\frac{17}{9}-\frac{4}{3}\right)\)
\(=\left(\frac{3}{10}+\frac{2}{5}\right)\div\frac{5}{9}\)
\(=\frac{7}{10}\div\frac{5}{9}=\frac{63}{50}\)
2, Chiều dài mảnh đất là:
\(\frac{25}{4}\div\frac{5}{4}=5\left(m\right)\)
Chu vi mảnh đất là:
\(\left(5+\frac{5}{4}\right)\times2=\frac{25}{2}\left(m\right)\)
\(Đs:...\)
Bài 1:
\(a,\frac{8}{9}-\frac{1}{3}:\frac{1}{2}\)
=\(\frac{8}{9}-\frac{2}{3}\)
=\(\frac{2}{9}\)
\(b,\left(\frac{3}{10}+\frac{4}{5}x\frac{1}{2}\right):\left(\frac{17}{9}-\frac{4}{3}\right)\)
=\(\left(\frac{3}{10}+\frac{4}{10}\right):\frac{5}{9}\)
=\(\frac{7}{10}:\frac{5}{9}\)
=\(\frac{63}{50}\)
Bài 2:
Chiều dài của mảnh đất hình chữ nhật đó là:
\(\frac{25}{4}:\frac{5}{4}=5\left(m^2\right)\)
Chu vi của mảnh đất hình chữ nhật đó là:
\(\left(\frac{5}{4}+5\right)x2=\frac{25}{2}\left(m\right)\)
Đáp số:\(\frac{25}{2} \left(m\right)\)
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\)
\(Ax2=2x\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\right)\)
\(Ax2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)
\(Ax2-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\right)-\left(\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{128}-\frac{1}{256}\right)\)
\(A=1-\frac{1}{256}\)
\(A=\frac{255}{256}\)
a) A= 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
A = 1 - 1/2 + 1/2- 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256 - 1/256 - 1/512
A = 1 - 1/512
A = 511/512
b) B = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
3B = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243
3B - B = 1 - 1/729
2B = 728/729
B = 364/729
a) A= 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
A = 1 - 1/2 + 1/2- 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256 - 1/256 - 1/512
A = 1 - 1/512
A = 511/512
b) B = 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
3B = 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243
3B - B = 1 - 1/729
2B = 728/729
B = 364/729
Tính \(S=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\)
Dùng sai phân như sau
\(2S-S=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{128}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\right)=1-\frac{1}{256}\)
Vậy \(S=1-\frac{1}{256}\)