\(VT=\frac{2^2-1^2}{1^2.2^2}+\frac{3^2-2^2}{2^2.3^2}+\frac{4^2-3^2}{3^2.4^2}+.....+\frac{10^2-9^2}{9^2.10^2}\)
\(=\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{2^2}-\frac{1}{3^2}+\frac{1}{3^2}-\frac{1}{4^2}+......+\frac{1}{9^2}-\frac{1}{10^2}\)
\(=1-\frac{1}{10^2}=\frac{99}{100}<1\)
Aj zúp đc then ìu nhìu nhêii
Chứng minh rằng : \(\frac{3}{1^2+2^2}\)+\(\frac{5}{2^2\cdot3^2}\)+\(\frac{7}{3^2\cdot4^2}\)+...+\(\frac{19}{9^2\cdot10^2}\)< 1
Chứng minh rằng
a, B = \(\frac{1\cdot2-1}{2!}+\frac{2\cdot3-1}{3!}+\frac{3\cdot4-1}{4!}+....+\frac{99\cdot100-1}{100!}< 2\)
c, C = \(\frac{3}{1^2\cdot2^2}+\frac{5}{2^2\cdot3^2}+\frac{7}{3^2\cdot4^2}+...+\frac{19}{9^2\cdot10^2}< 1\)
Chứng minh rằng \(A=\frac{3}{1^2\cdot2^2}+\frac{5}{2^2\cdot3^2}+\frac{7}{3^2\cdot4^2}+..........+\frac{19}{9^2\cdot10^2}< 1\)
Cm B=\(\frac{3}{1^2\cdot2^2}\)+\(\frac{5}{2^2\cdot3^2}\)+\(\frac{7}{3^2\cdot4^2}\)+...+\(\frac{19}{9^2\cdot10^2}\)<1
\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+..+\frac{1}{8\cdot9\cdot10}\cdot x=\frac{22}{45}\)thì x=
Tìm x biết: \(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{8\cdot9\cdot10}\cdot x=\frac{22}{45}\)Trình bày cách tính
tìm x biết : (\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+.....+\frac{1}{8\cdot9\cdot10}\)) x \(x=\frac{22}{45}\)
Tính \(A=\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\frac{1}{14\cdot19}+...+\frac{1}{44\cdot49}\right)\cdot\frac{1-3-5-7-...-49}{89}\)
\(B=\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^{10}\cdot6^{19}-7\cdot2^{29}\cdot27^6}-\frac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)
cho tổng M =\(\frac{3}{1^2\cdot2^2}+\frac{5}{2^2\cdot3^2}+\frac{7}{3^2\cdot4^2}+...+\frac{4019}{2009^2\cdot2010^2}.sosánhMvới1\)
