\(a,\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+....+\frac{4}{16.18}+\frac{4}{18.20}\)
\(=\frac{4}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{18}-\frac{1}{20}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(=2.\frac{9}{20}\)
\(=\frac{9}{10}\)
\(b,\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}\)
\(=\frac{9}{10}\)
a, \(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+..+\frac{4}{16.18}+\frac{4}{18.20}\)
\(=\frac{4}{2}\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{16}-\frac{1}{18}+\frac{1}{18}-\frac{1}{20}\right)\)
\(=2\cdot\left(\frac{1}{2}-\frac{1}{20}\right)\)
\(=2\cdot\frac{9}{20}=\frac{9}{10}\)
b, \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}=\frac{9}{10}\)
A, \(\frac{4}{2\times4}+\frac{4}{4\times6}+\frac{4}{6\times8}+.......+\frac{4}{16\times18}+\frac{4}{18\times20}\)
= \(2\times\) \(\left(\frac{4-2}{2\times4}+\frac{6-4}{4\times6}+\frac{8-6}{6\times8}+.......+\frac{18-16}{16\times18}+\frac{20-18}{18\times20}\right)\)
= \(2\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+.......+\frac{1}{16}-\frac{1}{18}+\frac{1}{18}-\frac{1}{20}\right)\)
= \(2\times\left(\frac{1}{2}-\frac{1}{20}\right)\)
= \(2\times\left(\frac{10}{20}-\frac{1}{20}\right)\)
= \(2\times\frac{9}{20}\)
= \(\frac{9}{10}\)
B, \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+.......+\frac{1}{90}\)
=\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+.......+\frac{1}{9\times10}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.......+\frac{1}{9}-\frac{1}{10}\)
= \(1-\frac{1}{10}\)
= \(\frac{9}{10}\)
CHÚC BẠN HỌC GIỎI VÀ ĐẠT ĐƯỢC NHIỀU THÀNH CÔNG TRONG CUỘC SỐNG.
Ta có:
a) \(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{16.18}+\frac{4}{18.20}\)
\(=\frac{4}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{16}-\frac{1}{18}+\frac{1}{18}-\frac{1}{20}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{20}\right)=2.\frac{9}{20}=\frac{9}{10}\)
b) \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{1}-\frac{1}{10}=\frac{9}{10}\)
a, 4/2x4+4/4x6+4/6x8+......+4/16x18+4/18x20=\(\frac{9}{10}\)
b, 1/2+1/6+1/12+1/20+......+1/90 =\(\frac{9}{10}\)
