cho A = \(\frac{9}{5^2}+\frac{9}{11^2}+\frac{9}{17^2}+....+\frac{9}{305^2}\)chứng minh A <\(\frac{3}{4}\)
Cho M = \(\frac{9}{5^2}+\frac{9}{11^2}+\frac{9}{17^2}+.........+\frac{9}{305^2}\)
Chứng minh M< \(\frac{3}{4}\)
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CMR: \(A=\frac{9}{5^2}\)+\(\frac{9}{11^2}+\frac{9}{17^2}+...+\frac{9}{305^2}<\frac{3}{4}\)
9/5^2<9/2.8
9/11^2<9/8.14
............
9/305^2<9/302.308
=>B<9/2.8+9/8.14+......+9/302.308
=9/6(1/2-1/8+1/8-1/14+..........+1/302-1/308
=3/2(1/2-1/308)<3/2.1/2=3/4(đpcm)
bạn ơi câu 2 từ dưới lên là sao zậy? *=*
cảm ơn Hồ Anh Khôi nha cho bn 1 k đó
Chứng minh rằng:
\(\frac{9}{5^2}+\frac{9}{11^2}+\frac{9}{17^2}+...+\frac{9}{305^2}< \frac{3}{4} \)
\(C=\frac{11}{9}+\frac{18}{16}+\frac{27}{25}+...+\frac{1766}{1764}\)
Chứng minh rằng:\(40\frac{20}{43}< C< 40\frac{20}{21}\)
\(D=\frac{8}{9}+\frac{24}{25}+\frac{48}{49}+...+\frac{200.202}{201^2}>99,75\)
\(E=\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{24}{2500}>48\)
Giải nhanh trong chiều này giùm mình nhé!
Cho A = \(\frac{9}{5^2}+\frac{9}{11^2}+\frac{9}{17^2}+.......+\frac{9}{409^2}\)
CMR A<\(\frac{1}{12}\)
\(A=\frac{\frac{1}{11}-\frac{1}{13}-\frac{1}{17}}{\frac{5}{11}-\frac{5}{13}-\frac{5}{17}}+\frac{\frac{-3}{3}-\frac{2}{9}-\frac{2}{27}+\frac{2}{81}}{\frac{7}{3}-\frac{7}{9}-\frac{7}{27}+\frac{7}{81}}\)
Chứng minh:\(A=\frac{11}{29}+\frac{9}{17}+\frac{10}{19}\) <2
Bài này chứng minh sao các bạn?
A = \(\frac{11}{29}+\frac{9}{17}+\frac{10}{19}\). Chứng minh A < 2.
Ta có: Trong 3 phân số thì \(\frac{9}{17}\)là phân số lớn nhất
\(\Rightarrow\frac{9}{17}+\frac{9}{17}+\frac{9}{17}>\frac{11}{29}+\frac{9}{17}+\frac{10}{19}\)
\(\Rightarrow\frac{9}{17}\times3>A\)
Mà \(\frac{9}{17}\times3=\frac{27}{17}< \frac{34}{17}=2\)
\(\Rightarrow2>\frac{9}{17}\times3>A\)
\(\Rightarrow A< 2\)
a,\(\frac{-5}{9}+\frac{8}{15}+\frac{-2}{11}+\frac{4}{-9}+\frac{7}{15}\)
b,\(\frac{5}{13}+\frac{-5}{17}+\frac{-20}{41}+\frac{8}{13}+\frac{-21}{41}\)
c,\(\frac{1}{5}+\frac{-2}{9}+\frac{-7}{9}+\frac{4}{5}+\frac{16}{17}\)
d,\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+......+\frac{2}{99.101}\)
a,\(=\frac{-5}{9}+\frac{8}{15}+\frac{-2}{11}+\frac{-4}{9}+\frac{7}{15}\)
\(\left(\frac{-5}{9}+\frac{-4}{9}\right)+\left(\frac{8}{15}+\frac{7}{15}\right)+\frac{-2}{11}\)
=-1+1+-2/11
=0+-2/11
=-2/11
b,\(=\left(\frac{5}{13}+\frac{8}{13}\right)+\left(\frac{-20}{41}+\frac{-21}{40}\right)+\frac{-5}{17}\)
=1+-1+-5/17
=0+-5/17
=-5/17
c,\(=\left(\frac{1}{5}+\frac{4}{5}\right)+\left(\frac{-2}{9}+-\frac{7}{9}\right)+\frac{16}{17}\)
=1+-1+16/17
=0+16/17
=16/17
d,\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)
\(=\frac{1}{3}-\frac{1}{101}=\frac{98}{303}\)
a.\(\frac{-5}{9}\)+\(\frac{8}{15}\)+\(\frac{-2}{11}\)+\(\frac{4}{-9}\)+\(\frac{7}{15}\)
=\(\frac{-5}{9}\)+\(\frac{4}{-9}\)+\(\frac{8}{15}\)+\(\frac{7}{15}\)+\(\frac{-2}{11}\)
=(\(\frac{-5}{9}\)+\(\frac{-4}{9}\))+(\(\frac{8}{15}\)+\(\frac{7}{15}\))+\(\frac{-2}{11}\)
=(-1)+1+\(\frac{-2}{11}\)
=0+\(\frac{-2}{11}\)
=\(\frac{-2}{11}\).
cho A=9/5 mũ 2+ 9/11 mũ 2+9/17 mũ 2+...+9/305 mũ 2 chứng minh A<3/4