Question

\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{200.202}\)

Answer 1

= \(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{200+202}\)

= \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-...+\frac{1}{200}-\frac{1}{202}\)

= \(\frac{1}{2}-\frac{1}{202}\)

= \(\frac{404}{202}-\frac{1}{202}\)

= \(\frac{403}{202}\)

Answer 2

bạn nhân 2 vào thì sẽ hiểu cách làm.

Answer 3

\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{200.202}\)

\(=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{200.202}\right)\)

\(=\frac{1}{2}.\left(\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{2}{200.202}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}...+\frac{1}{200}-\frac{1}{202}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{202}\right)\)

\(=\frac{1}{2}.\frac{50}{101}\)

\(=\frac{25}{101}\)

Answer 4

Đặt A=1/2.4+1/4.6+1/6.8+...+1/200.202
Ta có A=1/2.4+1/4.6+1/6.8+...+1/200.202
=>2.A=2(1/2.4+1/4.6+1/6.8+...+1/200.202)
=>2.A=2/2.4+2/4.6+2/6.8+...+2/200.202
=>2.A-A=(2/2.4+2/4.6+2/6.8+...+2/200.202)-(1/2.4+1/4.6+1/6.8+...+1/200.202)
=>A=1/2-1/4+1/4-1/6+1/6-1/8+...+1/200-1/202
=>A=1/2-1/202
=>A=100/202=50/101
Vậy A=50/101