a) \(\dfrac{2}{1^2}.\dfrac{6}{2^2}.\dfrac{12}{3^2}.\dfrac{20}{4^2}.\dfrac{30}{5^2}.....\dfrac{110}{10^2}.x=-20\)
b) \(\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2013}\right).x+2013=\dfrac{2014}{1}+\dfrac{2015}{2}+...+\dfrac{4025}{2012}+\dfrac{4026}{2013}\)
c) \(\left(\dfrac{1}{1.2}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right).x=\dfrac{2012}{51}+\dfrac{2012}{52}+...+\dfrac{2012}{99}+\dfrac{2012}{100}\)
chứng minh :
a) \(\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}>\dfrac{1}{4}\) b) \(\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{2013^2}+\dfrac{1}{2014}>\dfrac{1}{5}\)
chứng minh rằng :
a) \(\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}< \dfrac{1}{4}\) b)\(\dfrac{1}{5^2}+\dfrac{1}{6^5}+...+\dfrac{1}{2013^2}+\dfrac{1}{2014}>\dfrac{1}{5}\)
\(\left(6-2\dfrac{4}{5}\right)\cdot3\dfrac{1}{8}-1\dfrac{3}{5}:\dfrac{1}{4}\)
\(B=\dfrac{\left(\dfrac{11^2}{200}+0,415\right):0,01}{\dfrac{1}{12}-37,25+3\dfrac{1}{6}}\) tính B
tìm X
\(\dfrac{-9}{46}-4\dfrac{1}{23}:\left(3\dfrac{1}{4}-x:\dfrac{3}{5}\right)+2\dfrac{8}{23}=1\)
1.Tính nhanh:
A= \(\dfrac{\dfrac{2}{3}-\dfrac{1}{4}+\dfrac{5}{11}}{\dfrac{5}{12}+1-\dfrac{7}{11}}\)
2. Cho: B =\(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{19}\) .Hãy chứng tỏ rằng B > 1.
3. Rút gọn:
a) C= \(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)....\left(1-\dfrac{1}{20}\right)\)
b) D= \(1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2012}}\)
4. So sánh: E=\(\dfrac{20^{10}+1}{20^{10}-1}\) và F =\(\dfrac{20^{10}-1}{20^{10}-3}\)
5. Tính giá trị của biểu thức:
M= \(\dfrac{\dfrac{3}{5}+\dfrac{3}{7}-\dfrac{3}{11}}{\dfrac{4}{5}+\dfrac{4}{7}-\dfrac{4}{11}}\)
chứng minh rằng :
\(\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}< \dfrac{1}{4}\)
Bài 1: Rút gọn các phân số sau: a/ \(\dfrac{-63}{81}\), b/ \(\dfrac{5.6}{9.35}\), c/ \(\dfrac{7.2+8}{2.14.5}\)
Bài 2: Tìm X: a/ \(\dfrac{4}{7}\)-X = \(\dfrac{1}{2}\). X + \(\dfrac{2}{7}\); b/ X : \(3\dfrac{1}{5}\)= \(1\dfrac{1}{2}\); c/ X . \(\dfrac{3}{4}\)= \(-1\dfrac{5}{8}\)
Bài 3: Tính giá trị biểu thức: A= \(\dfrac{-3}{5}\)+ ( \(\dfrac{-2}{5}\)+ 2 ); B= \(\dfrac{3}{7}\)+ ( -\(\dfrac{1}{5}\) + \(\dfrac{-3}{7}\) ); C= ( -\(\dfrac{5}{24}\) + 0,75 + \(\dfrac{7}{12}\) ) : (-2. \(\dfrac{1}{8}\))
Bài 4: Tìm X: a/ ( \(2\dfrac{1}{3}\) + \(3\dfrac{1}{2}\) ) . X = \(-4\dfrac{1}{6}\) + \(3\dfrac{1}{7}\); b/ X : ( \(3\dfrac{1}{2}\) - \(5\dfrac{1}{6}\) ) = \(4\dfrac{1}{5}\) - \(6\dfrac{2}{3}\)
Các bạn giúp mình nha!
Bài 1: Tìm x, biết
a) 3\(\dfrac{1}{3}\) x+ 16\(\dfrac{3}{4}\) = -13,25
b) 3\(\dfrac{2}{7}\).x - \(\dfrac{1}{8}\) = 2\(\dfrac{3}{4}\)
c) x : 4\(\dfrac{1}{3}\) = - 2,5
d) (\(\dfrac{3x}{7}\) + 1) : (-4) = \(\dfrac{-1}{28}\)
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