Question

[nguyễn hoàng khánh an]

Tính nhanh:

     A=\(\frac{4}{2.4}\) + \(\frac{4}{4.6}\) + \(\frac{4}{6.8}\) +     . . .    + \(\frac{4}{2018.2020}\)

    B=  \(\frac{1}{18}\) +  \(\frac{1}{54}\) +   \(\frac{1}{108}\) +   . . .   + \(\frac{1}{990}\)

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CẢM ƠN MN NHIỀU!!!!

Answer 1

[Đặng Anh Thư]

A=\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2018.2020}\)

\(\frac{1}{2}\)A= \(\frac{1}{2}.\left(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2018.2020}\right)\)

\(\frac{1}{2}A\)= \(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2018.2020}\)

\(\frac{1}{2}A\)= \(\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{2020-2018}{2018.2020}\)

\(\frac{1}{2}A\)= \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\)

\(\frac{1}{2}A\)= \(\frac{1}{2}-\frac{1}{2020}\)

\(\frac{1}{2}A=\frac{1009}{2020}\)

\(A=\frac{1009}{2020}:\frac{1}{2}\)

\(A=\frac{1009}{1010}\)

Answer 2

[Lê Trần Ngọc Hằng]

a) Ta có 

A= 4/2*4+4/4*6+....+4/2018*2020

=> A= 2*(2/2*4+2/4*6+...+2*(2018*2020)

=> A= 2*(1/2-1/4+1/4-1/6+...+1/2018-1/2020)

=> A= 2*(1/2-1/2020)

=> A= 2* 1009/2020

=> A= 1009/1010

b) B= 1/18+1/54+1/108+...+1/990

=> B= 3/3*(1/18+1/54+1/108+..+1/990)

=> B= 1/3*( 3/3*6+3/6*9+...+3/30*33)

=> B= 1/3*(1/3-1/6+1/6-1/9+1/9-1/12+...+1/30-1/33)

=> B= 1/3*( 1/3-1/33)

=> B=1/3*10/33

=> B=10/99