Question

2-10/1*6 -10/6*11-10/11*16-10/16*21-.....-10/2016*2021

Answer 1

Lời giải:

Đặt phép tính trên là $A$
$2-A=\frac{10}{1.6}+\frac{10}{6.11}+\frac{10}{11.16}+....+\frac{10}{2016.2021}$
$2-A=2\left(\frac{6-1}{1.6}+\frac{11-6}{6.11}+\frac{16-11}{11.16}+...+\frac{2021-2016}{2016.2021}\right)$
$2-A=2\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{2016}-\frac{1}{2021}\right)$

$2-A=2\left(1-\frac{1}{2021}\right)=\frac{4040}{2021}$

$A=2-\frac{4040}{2021}=\frac{2}{2021}$