cho S = \(\frac{2}{2^1}+\frac{3}{2^2}+\frac{4}{2^3}+.....+\frac{2010}{2^{2009}}+\frac{2011}{2^{2010}}\)
SO SÁNH S VỚI 3
Những câu hỏi liên quan
So sánh S =\(\frac{2}{1×2×3}+\frac{2}{2×3×4}+\frac{2}{3×4×5}+...+\frac{2}{2010×2011×2012}\) với P=\(\frac{1}{2}\)
S=\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{2010.2011.2012}\)
=\(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{2010.2011}-\frac{1}{2011.2012}\)
=\(\frac{1}{2}-\frac{1}{2011.2012}< \frac{1}{2}\)(Vì \(\frac{1}{2011.2012}>0\))
=> S <\(\frac{1}{2}\)
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\(S=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+....+\frac{2}{2010.2011.2012}\)
\(S=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{2012-2010}{2010.2011.2012}\)
\(S=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2010.2011}-\frac{1}{2011.2012}\)
\(S=\frac{1}{1.2}-\frac{1}{2011.2012}=\frac{2023065}{4046132}\)
\(\text{Vì}\)\(\frac{2023065}{4046132}< \frac{1}{2}\Rightarrow S< P\)
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So sánh P và Q biết : P = 2010/2011 + 2011/2012 + 2012/2013 và Q = 2010+2011+2012/ 2011 +2012+2013
Chứng tỏ N < 1 với N = \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2009^2}+\frac{1}{2010^2}\)
Ta có: \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2010^2}
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1.Tính tổngSleft(frac{-1}{7}right)^0+left(frac{-1}{7}right)^1+left(frac{-1}{7}right)^2+...+left(frac{-1}{7}right)^{2007}2.Tìm x5^x+5^{x+2}6503.CMRfrac{1}{6} frac{1}{5^2}+frac{1}{6^2}+frac{1}{7^2}+...+frac{1}{100^2} frac{1}{4}4. Cho Afrac{1}{2010}+frac{2}{2009}+frac{3}{2008}+...+frac{2009}{2}+frac{2010}{1} Bfrac{1}{2}+frac{1}{3}+frac{1}{4}+...+frac{1}{2010}+frac{1}{2011}So sánh A và B
Đọc tiếp
1.Tính tổng
\(S=\left(\frac{-1}{7}\right)^0+\left(\frac{-1}{7}\right)^1+\left(\frac{-1}{7}\right)^2+...+\left(\frac{-1}{7}\right)^{2007}\)
2.Tìm x
\(5^x+5^{x+2}=650\)
3.CMR
\(\frac{1}{6}< \frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{100^2}< \frac{1}{4}\)
4. Cho \(A=\frac{1}{2010}+\frac{2}{2009}+\frac{3}{2008}+...+\frac{2009}{2}+\frac{2010}{1}\)
\(B=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2010}+\frac{1}{2011}\)
So sánh A và B
Tinh\(\frac{\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+...+\frac{2}{2009}+\frac{1}{2010}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2010}+\frac{1}{2011}}\)
Ghi lộn đề thiếu thì phải. Hình như thiếu phân số 1/2011
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Tính \(\frac{1}{2011}+\frac{2}{2010}+\frac{3}{2009}+...+\frac{2009}{3}+\frac{2010}{2}+\frac{2011}{1}\)
Ta có: A=\(\frac{1}{2011}+\frac{2}{2010}+\frac{3}{2009}+...+\frac{2009}{3}+\frac{2010}{2}+\frac{2011}{1}\)
=> A=\(\frac{2012-2011}{2011}+\frac{2012-2010}{2010}+...+\frac{2012-2}{2}+\frac{2012-1}{1}\)
=>A=\(\frac{2012}{2011}-1+\frac{2012}{2010}-1+...+\frac{2012}{2}-1+2012-1\)
=>A=\(2012\cdot\left(\frac{1}{2011}+\frac{1}{2010}+...+\frac{1}{2}\right)+1\)
=> A= \(2012\cdot\left(\frac{1}{2012}+\frac{1}{2011}+...+\frac{1}{2}\right)\)
ko biết có đúng hay ko nựa sai thì bỏ qua nha ^^
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dung r bn oi
con co cau p=1/2+1/3+...+1/2011+1/2012
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H = \(\frac{\frac{2010}{1}+\frac{2009}{2}+...+\frac{3}{2008}+\frac{2}{2009}+\frac{1}{2010}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}}\) =?
\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{2011}}{\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+....+\frac{1}{2010}}\)
\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+......+\frac{1}{2011}}{\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+....+\frac{1}{2010}}\)
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So sánh A với B, biết:
A = \(\frac{2009^{2009^{ }}+1}{2009^{2010}+1}\) và B = \(\frac{2009^{2010}-2}{2009^{2011}-2}\)
Ta có:
\(B=\dfrac{2009^{2010}-2}{2009^{2011}-2}\)
\(B< \dfrac{2009^{2010}-2+2011}{2009^{2011}-2+2011}\)
\(B< \dfrac{2009^{2010}+2009}{2009^{2011}+2009}\)
\(B< \dfrac{2009\left(2009^{2009}+1\right)}{2009\left(2009^{2010}+1\right)}\)
\(B< \dfrac{2009^{2009}+1}{2009^{2010}+1}\)
Mà \(A=\dfrac{2009^{2009}+1}{2009^{2010}+1}\)
\(\Rightarrow B< A\)
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Tính :
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}}{\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+...+\frac{1}{2010}}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}}{\frac{2010}{1}+\frac{2009}{2}+\frac{2008}{3}+...+\frac{1}{2010}}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+..+\frac{1}{2011}}{\left(\frac{2009}{2}+1\right)+\left(\frac{2008}{3}+1\right)+...+\left(\frac{1}{2010}+1\right)+1}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}}{\frac{2011}{2}+\frac{2011}{3}+...+\frac{2011}{2010}+\frac{2011}{2011}}\)
\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}}{2011\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2010}+\frac{1}{2011}\right)}\)
\(A=\frac{1}{2011}\)
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