Question

[Dương Diễm Quỳnh]

Câu hỏi của mình nè :

Tính nhanh nhé:

M=2/3x5+2/5x7+2/7x9+......+2/97x99

Answer 1

[Nguyễn Hưng Phát]

M=\(\frac{2}{3\times5}+\frac{2}{5\times7}+.............+\frac{2}{97\times99}\)

=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+..........+\frac{1}{97}-\frac{1}{99}\)

=\(\frac{1}{3}-\frac{1}{99}\)

=\(\frac{32}{99}\)

Answer 2

[Thắng Nguyễn]

\(\Leftrightarrow M=\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+\frac{2}{7}-\frac{2}{9}+...+\frac{2}{97}-\frac{2}{99}\)

\(\Rightarrow M=2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\right)\)

\(\Rightarrow M=2\left(\frac{1}{3}-\frac{1}{99}\right)\)

\(\Rightarrow M=2\times\frac{32}{99}\)

\(\Rightarrow M=\frac{64}{99}\)