Question

[Nguyễn Kim Chi]

tính A biết:

A= \(\dfrac{4}{2.5}\)+\(\dfrac{4}{5.8}\)+\(\dfrac{4}{8.11}\)+...+\(\dfrac{4}{65.68}\)=?

giúp mk nhé nhanh đẻ 2 tiếng nữa mk thi rùi

Answer 1

[Trần Thị Kim Chi]

A =\(\dfrac{4}{2.5}+\dfrac{4}{5.8}+\dfrac{4}{8.11}+...+\dfrac{4}{65.68}\)

A = \(\dfrac{4}{3}.\left(\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+...+\dfrac{3}{65.68}\right)\)

A = \(\dfrac{4}{3}.\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{65}-\dfrac{1}{68}\right)\)

A = \(\dfrac{4}{3}.\left[\dfrac{1}{2}-\left(\dfrac{1}{5}-\dfrac{1}{5}\right)-\left(\dfrac{1}{8}-\dfrac{1}{8}\right)-\left(\dfrac{1}{11}-\dfrac{1}{11}\right)-...-\left(\dfrac{1}{65}-\dfrac{1}{65}\right)-\dfrac{1}{68}\right]\)

A = \(\dfrac{4}{3}.\left[\dfrac{1}{2}-0-0-0-...-0-\dfrac{1}{68}\right]\)

A = \(\dfrac{4}{3}.\left[\dfrac{1}{2}-\dfrac{1}{68}\right]\)

A = \(\dfrac{4}{3}.\dfrac{33}{68}\)

A = \(\dfrac{11}{17}\)

Answer 2

[Trúc Linh]

1/3.(1/2.5+1.5.8+1/8.11+...+1/65.68)

=1/3.(1/2-1/5+1/5-1/8+1/8-1/11+...+1/65-1/68)

=1/3(1/2-1/68)

=1/3.33/68

=11/68

nhớ theo dõi mik nha