Question

tính tổng

E=5/25.27+5/27.29+5/29.31+...+5/72.75

Answer 1

Sửa đề: \(E=\dfrac{5}{25\cdot27}+\dfrac{5}{27\cdot29}+...+\dfrac{5}{73\cdot75}\)

\(=\dfrac{5}{2}\left(\dfrac{2}{25\cdot27}+\dfrac{2}{27\cdot29}+...+\dfrac{2}{73\cdot75}\right)\)

\(=\dfrac{5}{2}\left(\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}-\dfrac{1}{29}+...+\dfrac{1}{73}-\dfrac{1}{75}\right)\)

\(=\dfrac{5}{2}\left(\dfrac{1}{25}-\dfrac{1}{75}\right)=\dfrac{5}{2}\cdot\dfrac{2}{75}=\dfrac{5}{75}=\dfrac{1}{15}\)

Answer 2

E=5/25.27+5/27.29+5/29.31+...+5/72.75

=5 / (n . (n + 2))

=5 / (n . (n + 2)) = (5/2) . (1/n - 1/(n + 2))

E= (5/2) . (1/25 - 1/27) + (5/2) . (1/27 - 1/29) + (5/2) . (1/29 - 1/31) + ... + (5/2) . (1/72 - 1/75) 

E= (5/2) . (1/25 - 1/75)

E= (5/2) . (3/75 - 1/75)

E = (5/2) . (2/75)

E = 1/15

 

Answer 3

E= 5/25.27+5/27.29+5/29.31+...+5/72.75

= 5/2 x (2/25x27+ 2/27x29+....+2/73x75)

= 5/2 x (1/25-1/27+1/27-1/29+....+1/73-1/75)

= 5/2 x (1/25-1/75)

= 5/2 x 2/75

= 1/15