Question

[Phạm Hà Vy]

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)   \(\frac{4}{8.11}\) +    \(\frac{4}{11.14}\) +    \(\frac{4}{14.17}\)+ ........ +    \(\frac{4}{98.101}\)

Answer 1

[Thắng Nguyễn]

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