SAO THỔ

\(\frac{3}{18}+\frac{1}{18}=\frac{4}{18}=\frac{2}{9}\)hình tròn

Ta chọn phương án A

3/18+1/18=4/18=2/9

SR (A)

\(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{20}}{\dfrac{19}{1}+\dfrac{18}{2}+\dfrac{17}{3}+....+\dfrac{1}{19}}\)

\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{20}}{1+\left(\dfrac{18}{2}+1\right)+\left(\dfrac{17}{3}+1\right)+\left(\dfrac{1}{19}+1\right)}\)

\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{20}}{1+\dfrac{20}{2}+\dfrac{20}{3}+...+\dfrac{20}{19}}\)

\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{20}}{20.\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{19}+\dfrac{1}{20}\right)}\)

\(=\dfrac{1}{20}\)

bạn viết vậy khó hiểu quá bạn viết bằng kí tự phân số ik ạ

* Cách làm : Tử giữ nguyên,còn mẫu ta biến đổi như sau:
Mẫu : ( \(\frac{19}{1}\)+ 1 ) + ( \(\frac{18}{2}\)+ 1 ) + ( \(\frac{17}{3}\)+ 1 ) +...+ ( \(\frac{3}{17}\)+ 1 ) + ( \(\frac{2}{18}\)+ 1 ) + ( \(\frac{1}{19}\)+ 1 ) - 19  ( vì ta cộng với 19 số 1 nên phải trừ 19 )
= \(\frac{20}{1}\)+  \(\frac{20}{2}\)+  \(\frac{20}{3}\)+...+  \(\frac{20}{17}\)+  \(\frac{20}{18}\)+  \(\frac{20}{19}\)- 19
=  \(\frac{20}{2}\)+  \(\frac{20}{3}\)+...+  \(\frac{20}{17}\)+   \(\frac{20}{18}\)+  \(\frac{20}{19}\)+ ( \(\frac{20}{1}\)- 19)
=  \(\frac{20}{2}\)+  \(\frac{20}{3}\)+ ...+   \(\frac{20}{17}\)+  \(\frac{20}{18}\)+  \(\frac{20}{19}\)+  \(\frac{20}{20}\)
= 20.( \(\frac{1}{2}\)+  \(\frac{1}{3}\)+...+  \(\frac{1}{17}\)+  \(\frac{1}{18}\)+  \(\frac{1}{19}\)+  \(\frac{1}{20}\))
=> \(\frac{Tử}{Mâu}\)=  \(\frac{1}{20}\)

Phùng Quang Thịnh biến đổi sai 1 chỗ kìa 

-19 = \(\frac{20}{20}-20\)chứ mà bạn

Lời giải:

Đặt \(A=1+\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+...+\frac{18}{3^{18}}\)

\(\Rightarrow 3A=3+1+\frac{2}{3}+\frac{3}{3^2}+...+\frac{18}{3^{17}}\)

\(\Rightarrow 3A-A=3+\frac{2-1}{3}+\frac{3-2}{3^2}+\frac{4-3}{3^3}+..+\frac{18-17}{3^{17}}-\frac{18}{3^{18}}\)

\(2A=3+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{17}}-\frac{18}{3^{18}}\)

\(\Rightarrow 6A=9+1+\frac{1}{3}+\frac{1}{3^2}+..+\frac{1}{3^{16}}-\frac{18}{3^{17}}\)

\(\Rightarrow 6A-2A=7-\frac{18}{3^{17}}-\frac{1}{3^{17}}+\frac{18}{3^{18}}\)

\(\Leftrightarrow 4A=7+\frac{18}{3^{18}}-\frac{19}{3^{17}}=7-\frac{39}{3^{18}}\)

\(\Rightarrow A=\frac{1}{4}\left(7-\frac{39}{3^{18}}\right)\)