Question

Sao các bạn đổi được tên vậy?

Tính nhanh:  1/2.5+1/5.8+....+1/49.52

Answer 1

1/2.5 + 1/5.8 + ... + 1/49.52

= 1/3 . ( 3/2.5 + 3/5.8 + ... + 3/49.52 )

= 1/3 . ( 1/2 - 1/5 + 1/5 - 1/8 + ... + 1/49 - 1/52 )

= 1/3 . ( 1/2 - 1/52 )

= 1/3 . 25/52

= 25/156

Answer 2

\(\frac{1}{2.5}+\frac{1}{5.8}+....+\frac{1}{49.52}\)

\(=\frac{1}{3}.\left(\frac{3}{2.5}+\frac{3}{5.8}+...+\frac{3}{49.52}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{49}-\frac{1}{50}\right)\)

\(=\frac{1}{3}.\left(\frac{1}{2}-\frac{1}{52}\right)=\frac{1}{3}.\left(\frac{26}{52}-\frac{1}{52}\right)=\frac{1}{3}.\frac{25}{52}=\frac{25}{156}\)