Các câu hỏi tương tự
1, Tính \(\frac{1}{2}-\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{2}{4}+\frac{3}{4}\right)-\left(\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}\right)+...+\left(\frac{1}{100}+\frac{2}{100}+\frac{3}{100}+...+\frac{99}{100}\right)\)2,Tính \(\left(1-\frac{1}{2^2}\right)x\left(1-\frac{1}{3^2}\right)x\left(1-\frac{1}{4^2}\right)x...x\left(1-\frac{1}{n^2}\right)\)
Tính:
\(\frac{1}{2}-\left(\frac{1}{3}+\frac{2}{3}\right)+\left(\frac{1}{4}+\frac{2}{4}+\frac{3}{4}\right)-\left(\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}\right)+...+\left(\frac{1}{100}+\frac{2}{100}+\frac{3}{100}+...+\frac{99}{100}\right)\)
Chứng minh rằng:a)frac{1}{2^2}+frac{1}{3^2}+frac{1}{4^2}+...+frac{1}{2010^2}1b)frac{1}{2}+frac{2}{2^2}+frac{3}{2^3}+frac{4}{2^4}+...+frac{100}{2^{100}}2c)frac{1}{3}+frac{2}{3^2}+frac{3}{3^3}+...+frac{100}{3^{100}}frac{3}{4}d)frac{1}{3^3}+frac{1}{4^3}+frac{1}{5^3}+...+frac{1}{n^3}frac{1}{12}left(nin N;nge3right)e)frac{3}{4}+frac{5}{36}+frac{7}{144}+...+frac{2n+1}{n^2left(n+1right)^2}1 (n nguyên dương)g)frac{1}{31}+frac{1}{32}+frac{1}{33}+...+frac{1}{2048}3h)left(frac{2}{1}right)left(frac{4}{3}rig...
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Chứng minh rằng:
a)\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2010^2}\)<1
b)\(\frac{1}{2}+\frac{2}{2^2}+\frac{3}{2^3}+\frac{4}{2^4}+...+\frac{100}{2^{100}}\)<2
c)\(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{100}{3^{100}}\)<\(\frac{3}{4}\)
d)\(\frac{1}{3^3}+\frac{1}{4^3}+\frac{1}{5^3}+...+\frac{1}{n^3}\)<\(\frac{1}{12}\)\(\left(n\in N;n\ge3\right)\)
e)\(\frac{3}{4}+\frac{5}{36}+\frac{7}{144}+...+\frac{2n+1}{n^2\left(n+1\right)^2}\)<1 (n nguyên dương)
g)\(\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{2048}\)>3
h)\(\left(\frac{2}{1}\right)\left(\frac{4}{3}\right)\left(\frac{6}{5}\right)...\left(\frac{200}{199}\right)\)
Bài 1: Tìm x biết:a. frac{5}{1.6}+frac{5}{6.11}+...+frac{5}{left(5x+1right)left(5x+6right)}frac{2010}{2011}b. frac{7}{x}+frac{4}{5.9}+frac{4}{9.13}+frac{4}{13.17}+..+frac{4}{41.45}frac{29}{45}c. 1+frac{1}{3}+frac{1}{6}+frac{1}{10}+...+frac{1}{xleft(x+2right)}:2d. (x-20) . frac{frac{1}{2}+frac{1}{3}+..+frac{1}{2000}}{frac{1}{199}+frac{2}{198}+frac{3}{197}+...+frac{198}{2}+frac{199}{1}}frac{1}{2000}Bài 2: frac{a}{nleft(n+aright)}frac{1}{n}-frac{1}{n+a}left(n,aright)in NsaoBài 3:a)frac{3}{x}+frac{y...
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Bài 1: Tìm x biết:
a. \(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right)\left(5x+6\right)}=\frac{2010}{2011}\)
b. \(\frac{7}{x}+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+..+\frac{4}{41.45}=\frac{29}{45}\)
c. \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+2\right)}:2\)
d. (x-20) . \(\frac{\frac{1}{2}+\frac{1}{3}+..+\frac{1}{2000}}{\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}}=\frac{1}{2000}\)
Bài 2:
\(\frac{a}{n\left(n+a\right)}=\frac{1}{n}-\frac{1}{n+a}\left(n,a\right)\in Nsao\)
Bài 3:
a)\(\frac{3}{x}+\frac{y}{3}=\frac{5}{6}\)
b) \(\frac{x}{3}-\frac{4}{y}=\frac{1}{5}\)
c) \(\frac{x}{2}+\frac{y}{3}=\frac{x+y}{2+3}\)
d) \(\frac{x-1}{9}+\frac{1}{3}=\frac{1}{y+2}\)
Bài 1:Thực hiện phép tínha,75%-1frac{1}{2}+0,5:frac{5}{12}-left(frac{-1}{2}right)^2 b,left(frac{5}{7}.0,6-5:3frac{1}{2}right).left(40%-1,4right).left(-2right)^3Bài 2: Tính nhanh left(frac{-4}{5}+frac{4}{3}right)+left(frac{-5}{4}+frac{14}{5}right)-frac{7}{3}Bài 3:Tìm x biếta,frac{-2}{3}-frac{1}{3}.left(2x-5right)frac{3}{2} b,frac{2}{5}.x+frac{1}{2}frac{-3}{4} frac{1}{3}.x-8frac{1}{2} x-frac{1}{4}frac{5}{8}.frac{2}{3}Bài 4: Tìm...
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Bài 1:Thực hiện phép tính
\(a,75\%-1\frac{1}{2}+0,5:\frac{5}{12}-\left(\frac{-1}{2}\right)^2\) \(b,\left(\frac{5}{7}.0,6-5:3\frac{1}{2}\right).\left(40\%-1,4\right).\left(-2\right)^3\)
Bài 2: Tính nhanh
\(\left(\frac{-4}{5}+\frac{4}{3}\right)+\left(\frac{-5}{4}+\frac{14}{5}\right)-\frac{7}{3}\)
Bài 3:Tìm x biết
\(a,\frac{-2}{3}-\frac{1}{3}.\left(2x-5\right)=\frac{3}{2}\) \(b,\frac{2}{5}.x+\frac{1}{2}=\frac{-3}{4}\) \(\frac{1}{3}.x-8=\frac{1}{2}\) \(x-\frac{1}{4}=\frac{5}{8}.\frac{2}{3}\)
Bài 4: Tìm x biết
\(a,\left(\frac{3}{4}.x+2\frac{1}{2}\right).\frac{-2}{3}=\frac{1}{8}\) \(b,\frac{1}{3}.x-0,5=0,75\)
Bài 5: Tìm x biết
\(a,\frac{2}{5}+\frac{3}{5}.\left(3x-3,7\right)=-\frac{53}{10}\) \(b,5,2.x+7\frac{2}{5}=6\frac{3}{4}\) \(2,4:\left(\frac{-1}{2}-x\right)=1\frac{3}{5}\)
Bài 6:Tìm số tự nhiên x,biết: \(\left(x-5\right).\frac{30}{100}=\frac{20.x}{100}+5\)
Mik đang cần gấp giúp mik nha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Cho M = \(\frac{\left(\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{99}{1}\right)}{\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.....+\frac{1}{100}\right)}\);
N = \(\frac{\left(92-\frac{1}{9}-\frac{2}{10}-\frac{3}{11}-...-\frac{92}{100}\right)}{\left(\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+....+\frac{1}{500}\right)}\)
Tìm tỉ số phần trăm của M và N
Tính nhanh :
A = \(\left(\frac{2}{3}+\frac{3}{4}+....+\frac{99}{100}\right)\cdot\left(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+....+\frac{98}{99}\right)-\left(\frac{1}{2}+\frac{2}{3}+...+\frac{99}{100}\right)\cdot\left(\frac{2}{3}+\frac{3}{4}+...+\frac{98}{99}\right)\)
Tìm x thoả mãn:a)frac{1}{2}x-frac{3}{4}x-frac{7}{3}-frac{5}{6}b)frac{4}{5}x-x-frac{3}{2}x+frac{4}{3}frac{1}{2}-frac{6}{5}c)frac{1}{1.2}+frac{1}{2.3}+......+frac{1}{x.left(x+1right)}frac{2009}{2010}d)frac{1}{3}+frac{1}{6}+frac{1}{10}+...+frac{2}{xleft(x+1right)}1frac{2013}{2015}e)frac{1}{3.5}+frac{1}{5.7}+.....+frac{1}{left(2x+1right)left(2x+3right)}frac{100}{609}
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Tìm x thoả mãn:
a)\(\frac{1}{2}x-\frac{3}{4}x-\frac{7}{3}=-\frac{5}{6}\)
b)\(\frac{4}{5}x-x-\frac{3}{2}x+\frac{4}{3}=\frac{1}{2}-\frac{6}{5}\)
c)\(\frac{1}{1.2}+\frac{1}{2.3}+......+\frac{1}{x.\left(x+1\right)}=\frac{2009}{2010}\)
d)\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=1\frac{2013}{2015}\)
e)\(\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{100}{609}\)
Cho M =\(\frac{3\div\frac{2}{5}-0,09:\left(0,15-2\frac{1}{2}\right)}{0,32+0,03-\left(5,3-3,88\right)+0,67}\)
N =\(\frac{\left(2,1-1,965\right):\left(1,2.0,045\right)}{0,00325:0,013}-\frac{1:0,25}{1,6.0,625}\)
Tìm \(\frac{12}{100}\) của tổng \(\frac{3}{4}.M+\frac{1}{3}.N\)