Tính tổng:
a) \(\frac{1}{2.4}\)+ \(\frac{1}{4.6}\) + \(\frac{1}{6.8}\) + ....... + \(\frac{1}{98.100}\)
b) \(\frac{1}{1.5}\) + \(\frac{1}{5.9}\) + \(\frac{1}{9.13}\) + ........ + \(\frac{1}{201.205}\)
c) \(\frac{6}{3.5}\) + \(\frac{6}{5.7}\)+ \(\frac{6}{7.9}\) + .......... + \(\frac{6}{97.99}\)
d) \(\frac{4}{8.11}\) + \(\frac{4}{11.14}\) + \(\frac{4}{14.17}\)+ ........ + \(\frac{4}{98.101}\)
a)\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(=\frac{1}{2}\cdot\frac{49}{100}\)
\(=\frac{49}{200}\)
b)\(=\frac{1}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{201}-\frac{1}{205}\right)\)
\(=\frac{1}{4}\left(1-\frac{1}{205}\right)\)
\(=\frac{1}{4}\cdot\frac{204}{205}\)
\(=\frac{51}{205}\)
c)\(=3\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=3\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(=3\cdot\frac{32}{99}\)
\(=\frac{32}{33}\)
d)tương tự bạn nhân với 4/3 nhé
