Question

Tính

5/2 . 3 + 5/3 .4+5/4 .5 +.......+5/99.100

/ là phần nha .5/2 là 5 phần 2

Answer 1

\(\frac{5}{2.3}+\frac{5}{3.4}+\frac{5}{4.5}+...+\frac{5}{99.100}\)

\(=5.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{99.100}\right)\)

\(=5.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-....-\frac{1}{100}\right)\)

\(=5.\left(\frac{1}{2}-\frac{1}{100}\right)=\frac{5.49}{100}=\frac{49}{20}\)

Answer 2

5/2 . 3 + 5/3 .4+5/4 .5 +.......+5/99.100

= ( 1 / 2.3 + 1 /3.4 + 1 / 4.5 + ..... + 5 / 99. 100 ). 5

= 5 ( 1 / 2 - 1 / 3 + 1 / 3 - 1 / 4 + 1 / 4 - 1 / 5 +.... + 1 / 99 - 1 / 100 )

= 5 ( 1 / 2 - 1 / 100 )

= 5 . 49 / 100

= 49 / 20