cmr A= 1/2+1/3+...+1/511 <8
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A=1-1/2+1-1/4+...+1-1/2024
=10-(1/2+1/4+...+1/2024)
Đặt B=1/2+1/4+...+1/1024
=>2B=1+1/2+...+1/512
=>B=1-1/1024=1023/1024
=>A=10-1023/1024=9217/1024
Bài 1:
a) \(\left(\frac{5}{19}-\frac{1}{511}+\frac{7}{12}\right)-\left(-\frac{1}{511}-\frac{1}{2}+\frac{5}{19}\right)\)
= \(\frac{5}{19}-\frac{1}{511}+\frac{7}{12}+\frac{1}{511}+\frac{1}{2}-\frac{5}{19}\)
= \(\left(\frac{5}{19}-\frac{5}{19}\right)+\left(\frac{1}{511}-\frac{1}{511}\right)+\left(\frac{7}{12}+\frac{1}{2}\right)\)
= 0 + 0 + \(\frac{13}{12}\)
= \(\frac{13}{12}\).
b) \(-\left(\frac{13}{25}-\frac{4}{191}+\frac{2}{51}\right)+\left(\frac{4}{191}+\frac{2}{51}+\frac{3}{5}\right)\)
= \(-\frac{13}{25}+\frac{4}{191}-\frac{2}{51}+\frac{4}{191}+\frac{2}{51}+\frac{3}{5}\)
= \(\left(-\frac{13}{25}+\frac{3}{5}\right)+\left(\frac{4}{191}+\frac{4}{191}\right)+\left(\frac{2}{51}-\frac{2}{51}\right)\)
= \(\frac{2}{25}+\frac{8}{191}+0\)
= \(\frac{582}{4775}\).
Mình chỉ làm câu a) và câu b) thôi nhé.
Chúc bạn học tốt!
A=1/2+1/4+1/8.....+1/256+1/512
2A=1+1/2+1/4+1/8...1/256
A=(1+1/2+1/4+1/8...1/256)-(1/2+1/4+1/8.....+1/256+1/512)
A=1-1/512
A=511/512
511/512
\(x:\dfrac{1}{2}+x:\dfrac{1}{4}+x:\dfrac{1}{8}+...+x:\dfrac{1}{512}=511\\ 2x+4x+8x+..+512x=511\\ x\left(2+4+8+...+512\right)=511\\ x\left(2^1+2^2+2^3+...+2^9\right)=511\\ \)
Gọi \(S=2^1+2^2+2^3+...+2^9\)
\(2S=2^2+2^3+2^4+...+2^{10}\\ 2S-S=\left(2^2+2^3+2^4+...+2^{10}\right)-\left(2^1+2^2+2^3+...+2^9\right)\\ S=2^{10}-2\)
\(x\left(2^{10}-2\right)=511\\ 2x\left(2^9-1\right)=511\\ 2x\left(512-1\right)=511\\ 2x\cdot511=511\\ 2x=1\\ x=\dfrac{1}{2}\)
Vậy \(x=\dfrac{1}{2}\)