Question

tính nhanh

1/2*3 + 1/6*5 + 1/10*7 + 1/14*9+..+ 1/198*101

Answer 1

\(\frac{1}{2.3}+\frac{1}{6.5}+\frac{1}{10.7}+\frac{1}{14.9}+...+\frac{1}{198.101}\)

= \(2.\left(\frac{1}{2.6}+\frac{1}{6.10}+\frac{1}{10.14}+\frac{1}{14.18}+...+\frac{1}{198.202}\right)\)

= \(2.\frac{1}{4}.\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+\frac{1}{14}-\frac{1}{18}+...+\frac{1}{198}-\frac{1}{202}\right)\)

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

= \(\frac{1}{2}.\frac{50}{101}\)

= \(\frac{25}{101}\)

Answer 2

A=25/101