Question

[Phi Yến Trần Phan]

tính : \(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{36}+\frac{1}{45}\)

Answer 1

[Minh Hiền Trần]

Đặt A = 1/2 + 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/36 + 1/45

=> 1/2A = 1/4 + 1/6 + 1/12 + 1/20 + 1/30 + ... + 1/72 + 1/90

= 1/4 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/8.9 + 1/9.10

= 1/4 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10

= 1/4 + 1/2 - 1/10

= 5/20 + 10/20 - 2/20

= 13/20

=> A = 13/20 : 1/2 = 13/10

Answer 2

[Quốc Đạt]

Đặt A = 1/2 + 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/36 + 1/45

=> 1/2A = 1/4 + 1/6 + 1/12 + 1/20 + 1/30 + ... + 1/72 + 1/90

= 1/4 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/8.9 + 1/9.10

= 1/4 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10

= 1/4 + 1/2 - 1/10 

= 5/20 + 10/20 - 2/20 = 13/20

=> A = 13/20 : 1/2 = 13/10