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\(A=\frac{3}{1^2x2^2}+\frac{5}{2^2x3^2}+\frac{7}{3^2x4^2}+......+\frac{39}{19^2x20^2}\)
Tính A
Chứng minh \(\frac{3}{1^2x2^2}+\frac{5}{2^2x3^2}+\frac{7}{3^2x4^2}+...+\frac{2013}{1006^2x1007^2}\) < 1
Tính:a) frac{left(1+frac{17}{1}right).left(1+frac{17}{2}right).left(1+frac{17}{3}right).....left(1+frac{17}{19}right)}{left(1+frac{19}{1}right).left(1+frac{19}{2}right).left(1+frac{19}{3}right).....left(1+frac{19}{17}right)}b) frac{frac{-6}{5}+frac{6}{19}-frac{6}{23}}{frac{9}{5}-frac{9}{19}+frac{9}{23}}c) frac{frac{1}{6}-frac{1}{39}+frac{1}{51}}{frac{1}{8}-frac{1}{52}+frac{1}{68}}d) frac{frac{2}{3}-frac{2}{5}-frac{2}{7}+frac{2}{11}}{frac{13}{3}-frac{13}{5}-frac{13}{7}+frac{13}{11}}e) frac{frac{1...
Đọc tiếp
Tính:
a) \(\frac{\left(1+\frac{17}{1}\right).\left(1+\frac{17}{2}\right).\left(1+\frac{17}{3}\right).....\left(1+\frac{17}{19}\right)}{\left(1+\frac{19}{1}\right).\left(1+\frac{19}{2}\right).\left(1+\frac{19}{3}\right).....\left(1+\frac{19}{17}\right)}\)
b) \(\frac{\frac{-6}{5}+\frac{6}{19}-\frac{6}{23}}{\frac{9}{5}-\frac{9}{19}+\frac{9}{23}}\)
c) \(\frac{\frac{1}{6}-\frac{1}{39}+\frac{1}{51}}{\frac{1}{8}-\frac{1}{52}+\frac{1}{68}}\)
d) \(\frac{\frac{2}{3}-\frac{2}{5}-\frac{2}{7}+\frac{2}{11}}{\frac{13}{3}-\frac{13}{5}-\frac{13}{7}+\frac{13}{11}}\)
e) \(\frac{\frac{1}{1009}+\frac{1}{1010}+\frac{1}{1011}+...+\frac{1}{2017}}{1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}+\frac{1}{2017}}\)
2) CMR: \(\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+...+\frac{1}{2^{800}}< \frac{1}{3}\)
Tính Hợp Lí:
1/ \(\frac{1}{7}.\frac{1}{3}+\frac{1}{7}.\frac{1}{2}-\frac{1}{7}\)
2/\(\frac{3}{5}.\frac{7}{9}+\frac{3}{5}.\frac{2}{9}+\frac{3}{5}\)
3/ \(21\left(\frac{1}{7}-\frac{1}{5}+\frac{19}{21}\right)\)
Chứng minh rằng \(A=\frac{3}{1^2\cdot2^2}+\frac{5}{2^2\cdot3^2}+\frac{7}{3^2\cdot4^2}+..........+\frac{19}{9^2\cdot10^2}< 1\)
CMR : A > 1
A= \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}\)
1.\(\left(\frac{-6}{5}+\frac{6}{16}-\frac{6}{23}\right):\left(\frac{9}{5}-\frac{9}{19}+\frac{9}{23}\right)\)
2.\(\frac{\frac{3}{7}-\frac{3}{-11}+\frac{3}{13}}{\frac{5}{7}-\frac{5}{11}+\frac{5}{13}}+\frac{0,5-\frac{1}{3}+\frac{1}{4}}{\frac{-3}{2}+1-\frac{3}{4}}\)
chứng minh rằng:
a) A= \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}\)<1
b)B=\(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{4^4}+...+\frac{100}{3^{100}}< \frac{3}{4}\)
\(CM:\frac{3}{1^2+2^2}+\frac{5}{2^2+3^2}+\frac{7}{3^2+4^2}+...+\frac{19}{9^2+10^2}< 1\)