Question

 A ) a = 1/2 + 1/6  + 1/18 + 1/54  + 1/162
B ) 1/2 + 1/6 + 1/ 12 + 1/ 20 + ...+ 1/ 9900
C ) 20.2*5.1-30.3*3.4+14.56/ 14.58*460+7.29 *540*2 
* đây là dấu nhân nhé

Answer 1

A) bạn xem lại đề ạ

B) 1/2 + 1/6 + 1/ 12 + 1/ 20 + ...+ 1/ 9900
=1/2+1/6+1/12+...+1/9900
=1/1.2+1/2.3+1/3.4+...+1/99.100
=1/1-1/2+1/2-1/3+...+1/99-1/100
=1/1-1/100
=99/100
C) Biến đổi tử số và mẫu số ta có

- Tử số: 20,2 x 5,1 - 30,3 x 3,4 + 14,58
          = 103,02 - 103,02 + 14,58
          = 14,58
- Mẫu số: 14,58 x 460 + 7,29 x 540 x 2
          = 14,58 x 460 + 14,58 x 540
          = 14,58 x (460 + 540)
          = 14,58 x 1000
          = 14580

Thay vào ta có: = 14,58 : 14580
                         = 0,001
Vậy 20.2*5.1-30.3*3.4+14.56/ 14.58*460+7.29 *540*2 = 0,001.

Answer 2

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\)

\(\Rightarrow A=\frac{1}{2}\left(1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\right)\)

Gọi  \(B=1+\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\)

\(\Rightarrow\frac{1}{3}B=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+\frac{1}{243}\)

\(\Rightarrow B-\frac{1}{3}B=1-\frac{1}{243}\)

\(\Rightarrow\frac{2}{3}B=\frac{242}{243}\)

\(\Rightarrow B=\frac{121}{81}\)

Suy ra  \(A=\frac{1}{2}B=\frac{1}{2}.\frac{121}{81}=\frac{121}{162}\)

Answer 3

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)