[Hỗ trợ giải Toán lớp 6 trên mạng] – Tính hợp lý biểu thức A = 10/56 + 10/140 + 10/260 + …+ 10/1400.
Giải:
Ta có: A = 10/56 + 10/140 + 10/260 + …+ 10/1400
<=> A = 20/8.14 + 20/14.20 + 20/20.26 + …+ 20/50.56
20/8.14 = (10/3)*(1/8 – 1/14)
20/14.20 = (10/3)*(1/14 – 1/20)
20/20.26= (10/3)*(1/20 – 1/26)
…
20/50.56 = (10/3)*(1/50 – 1/56)
=> A = (10/3)*(1/8 – 1/14) + (10/3)*(1/14 – 1/20) + (10/3)*(1/20 – 1/26) + …+ (10/3)*(1/50 – 1/56)
A = (10/3)*(1/8 – 1/14 + 1/14 – 1/20 + 1/20 – 1/26 + …+ 1/50 – 1/56)
A = (10/3)*(1/8 – 1/56)
A = (10/3)*(6/56)
A = 5/14.
