\(\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+....+\frac{1}{2014.2016}\)
\(=\frac{1}{2}\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+....+\frac{2}{2014.2016}\right)\)
\(=\frac{1}{2}\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+....+\frac{1}{2014}-\frac{1}{2016}\right)\)
\(=\frac{1}{2}\left(\frac{1}{4}-\frac{1}{2016}\right)\)
\(=\frac{503}{4032}\)
Tính \(\frac{1}{6\times10}+\frac{1}{7\times9}+\frac{1}{8\times8}+\frac{1}{9\times7}+\frac{1}{10\times6}\)
\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+\frac{1}{8\times9}+\frac{1}{9\times10}\)
C=\(\frac{1\times5\times6+2\times10\times12+24\times8\times10}{1\times3\times5+2\times6\times10+8\times6\times20}\)
Thực hiện phép tính :
b) \(\frac{5}{4\times6}\)+ \(\frac{5}{6\times8}\)+ \(\frac{5}{8\times10}\)+ ... + \(\frac{5}{298\times300}\)
Bài 4: Tính nhanh:
a, A =\(\left(\frac{84}{13}\right)^2+\left(\frac{35}{13}\right)^2\)
b, B = \(\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}\div\frac{3+\frac{3}{13}+\frac{3}{169}+\frac{3}{91}}{7+\frac{7}{13}+\frac{7}{169}+\frac{7}{91}}\)
c, C =\(\frac{1\times2+2\times4+3\times6+4\times8+5\times10}{3\times4+6\times8+9\times12+12\times16+15\times20}\)
Tìm x biết \(\frac{4}{2\times4}+\frac{4}{4\times6}+\frac{4}{6\times8}+...+\frac{4}{2008\times2010}+x=\frac{-1}{1005}\)
Tính\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...\frac{1}{2014\times2015\times2016}\)
CHO A = \(\frac{2\times9\times8+3\times12\times10+4\times15\times12+...+98\times297\times200}{2\times3\times4+3\times4\times5+4\times5\times6+...+98\times99\times100}\)
TÍNH A\(^2\)
\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{2014\times2015\times2016}=?\)
