\(Cm:\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{1990^2}< \frac{3}{4}\)
Help me! :((
KN
Những câu hỏi liên quan
CMR:\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{1990^2}< \frac{3}{4}\)
Chứng minh rằng
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+....+\frac{1}{1990^2}< \frac{3}{4}\)
chững minh :
a) A= 1+\(\frac{1}{2^3}+\frac{1}{3^2}+\frac{1}{4^2}+.....+\frac{1}{100^2}< 2\)2
b)B=1+\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}< 6\)
giúp với help me
Câu a) Mik chữa lại một chút
Ta có: \(\frac{1}{2^2}< \frac{1}{1\cdot2}\); \(\frac{1}{3^2}< \frac{1}{2\cdot3}\);.......; \(\frac{1}{100^2}< \frac{1}{99\cdot100}\)
Suy ra: \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{99\cdot100}\)
Suy ra: \(VT< \frac{1}{1}-\frac{1}{100}=\frac{99}{100}< 1\)
Vậy : \(VT+1< 1+1=2\)
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Tìm x:
\(x.\frac{1}{2}-x.\frac{2}{3}+x.\frac{3}{4}-x.\frac{5}{6}=\frac{5}{6}-\frac{3}{4}+\frac{2}{3}-\frac{1}{2}\)
help me pleas
x . \(\frac{1}{2}\)- x.\(\frac{2}{3}\) + x.\(\frac{3}{4}\)- x. \(\frac{5}{6}\) = \(\frac{5}{6}\) -\(\frac{3}{4}\) + \(\frac{2}{3}\) -\(\frac{1}{2}\)
x . \(\frac{1}{2}\)- x.\(\frac{2}{3}\) + x.\(\frac{3}{4}\)- x. \(\frac{5}{6}\) = \(\frac{10}{12}\)-\(\frac{9}{12}\)+\(\frac{8}{12}\)-\(\frac{6}{12}\)
x . \(\frac{1}{2}\)- x.\(\frac{2}{3}\) + x.\(\frac{3}{4}\)- x. \(\frac{5}{6}\)= \(\frac{1}{4}\)=> x. (\(\frac{1}{2}\)- \(\frac{2}{3}\) + \(\frac{3}{4}\)- \(\frac{5}{6}\)) = \(\frac{1}{4}\)=> x.( \(\frac{6}{12}\)- \(\frac{8}{12}\)+\(\frac{9}{12}\)-\(\frac{10}{12}\))= \(\frac{1}{4}\)=> x. \(\frac{-1}{4}\)=\(\frac{1}{4}\)=> x = \(\frac{1}{4}\): \(\frac{-1}{4}\)=> x = -1
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=>x.(1/2-2/3+3/4)=1/4
=>x.7/12=1/4
=>x=1/4:7/12
=>x=1/4.12/7
=>x=3/7
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CMR:
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{1990^2}< \frac{3}{4}\)
Các bạn giúp mk với
1/2.2<1/1.2 1/3.3<2.3 ... 1/1990.1990<1/1990.1989 => 1/2^2+... +1/1990^2< 1/1.2+1/2.3+...+ 1/1990+1989
=>1/2^2+...+1/1990^2<1/1990<3/4
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Chứng minh rằng
\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{1990^2}\) < \(\frac{3}{4}\)
1,CMR:\(1-\frac{1}{2}-\frac{1}{3}-\frac{1}{4}-...-\frac{1}{1990}=\frac{1}{996}+\frac{1}{997}+\frac{1}{1990}\)
a) \(\left(-3+\frac{3}{x}-\frac{1}{3}\right)\div\left(1+\frac{2}{5}+\frac{2}{3}=-\frac{5}{4}\right)\)
b) \(-\frac{3x}{4}\times\left(\frac{1}{x}+\frac{2}{7}\right)=0\)
c) \(3-\frac{1-\frac{1}{2}}{1+\frac{1}{x}}=2\frac{2}{3}\)
Help me!!! Cần gấp trong 10 phút.
H24
3 tháng 12 2015 lúc 14:28
Tính A = \(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+.....+\frac{1}{1+2+3+.....+2014}\)
Help me ~~~~
\(\frac{1}{2}A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2014.2015}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+..+\frac{1}{2014}-\frac{1}{2015}\)
\(=\frac{1}{2}-\frac{1}{2015}=\frac{2013}{4030}=>A=\frac{2013}{4030}:2=\frac{2013}{2015}\)
tick nhe
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