1) Tìm số nguyên m để:
a) \(\left|3m-1\right|< 3\)
b) \(2m-3⋮3m+1\)
2) Cho \(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+......+\left(\frac{3}{4}\right)^{2010}\)
Chứng minh A < 1
Những câu hỏi liên quan
1) Tìm số nguyên m để:
a) \(\left|3m-1\right|< 3\)
b) \(2m-3⋮3m+1\)
2) Cho \(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+......+\left(\frac{3}{4}\right)^{2010}\)\
Chứng minh A < 1
cho A = \(1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
chứng tỏ A ko phải là số nguyên
cho \(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
CHỨNG TỎ A KO PK LÀ SỐ NGUYÊN
\(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
\(\Rightarrow\frac{3}{4}A=\frac{3}{4}-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^2+-\left(\frac{3}{4}\right)^4+...+\left(\frac{3}{4}\right)^{2010}-\left(\frac{3}{4}\right)^{2011}\)
\(\Rightarrow\frac{3}{4}A+A=\frac{3}{4}-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^2+-\left(\frac{3}{4}\right)^4+...+\left(\frac{3}{4}\right)^{20010}-\left(\frac{3}{4}\right)^{2011}\)
\(+1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
\(\Rightarrow\frac{7}{4}A=1-\left(\frac{3}{4}\right)^{2011}\)
\(\Rightarrow A=\frac{4}{7}-\frac{4}{7}.\left(\frac{3}{4}\right)^{2011}\)
\(\Rightarrow A=\frac{4}{7}-\frac{3^{2011}}{7.4^{2010}}\)
Vậy A không là số tự nhiên
Số nguyên chứ không pk stn nhé, nhầm
Sửa bài:
\(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
=> \(\frac{3}{4}.A=\frac{3}{4}-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^3-\left(\frac{3}{4}\right)^4+\left(\frac{3}{4}\right)^5-...-\left(\frac{3}{4}\right)^{2010}+\left(\frac{3}{4}\right)^{2011}\)
=> \(A+\frac{3}{4}A=1+\left(\frac{3}{4}\right)^{2011}\)
<=> \(\frac{7}{4}A=1+\left(\frac{3}{4}\right)^{2011}\)
=> \(A=\frac{4}{7}+\frac{4}{7}.\left(\frac{3}{4}\right)^{2011}\)không phải là số nguyên .
Chứng tỏ A không phải số nguyên
A=\(1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
Cho \(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
Chứng tỏ A ko phải là số nguyên
\(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+...+\left(\frac{3}{4}\right)^{2010}\)
\(\frac{3}{4}A=\frac{3}{4}-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^3-...-\left(\frac{3}{4}\right)^{2011}\)
\(\frac{3}{4}A-1=-\left[1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+...+\left(\frac{3}{4}\right)^{2010}\right]-\left(\frac{3}{4}\right)^{2011}\)
\(\frac{3}{4}A-1=A-\left(\frac{3}{4}\right)^{2011}\)
\(\frac{3}{4}A-A=-\left(\frac{3}{4}\right)^{2011}+1\)
\(-\frac{1}{4}A=1-\left(\frac{3}{4}\right)^{2011}\)
\(A=\frac{1-\left(\frac{3}{4}\right)^{2011}}{-\frac{1}{4}}=1:-\frac{1}{4}-\left(\frac{3}{4}\right)^{2011}:\left(-\frac{1}{4}\right)=-4+3\cdot\left(\frac{3}{4}\right)^{2010}\)
=>A không phải là số nguyên
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Cho A=\(1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-......-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
Chứng minh A không phải số nguyên
cho A=\(1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\) chứng tỏ A không phải là số nguyên
Cho:
\(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
Chứng tỏ A không phải là số nguyên
\(\frac{3}{4}A=\frac{3}{4}-\left(\frac{3}{4}\right)^2+\left(\frac{3}{4}\right)^3-\left(\frac{3}{4}\right)^4+\left(\frac{3}{4}\right)^5-....-\left(\frac{3}{4}\right)^{2010}\)
\(A+\frac{3}{4}A=1-\left(\frac{3}{4}\right)^{2010}\)
\(\frac{7}{4}A=1-\left(\frac{3}{4}\right)^{2010}\)
\(A=\frac{4}{7}\left(1-\left(\frac{3}{4}\right)^{2010}\right)khong\:làsốnguyên\)
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Cho:
\(A=1-\frac{3}{4}+\left(\frac{3}{4}\right)^2-\left(\frac{3}{4}\right)^3+\left(\frac{3}{4}\right)^4-...-\left(\frac{3}{4}\right)^{2009}+\left(\frac{3}{4}\right)^{2010}\)
Chứng minh A ko phải số nguyên