\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{9}-\frac{1}{2009}\right)\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{2000}{18081}\right)\)

\(A=\frac{1}{19}+\frac{200}{2009}\)

\(A=\frac{5809}{38171}\)

MK ko chắc nhé =v ( mấy bước quy đồng lằng nhằng ko làm âu )

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)=\frac{1}{19}+\frac{9}{10}\cdot\frac{1990}{38171}=\frac{1}{19}+\frac{1791}{38171}=\frac{200}{2009}\)

\(\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}.\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}.\left(\frac{1}{19}-\frac{1}{2009}\right)\)

b tự làm nốt nhé

\(\frac{1}{9.19}+\frac{1}{19.29}+\frac{1}{29.39}+...+\frac{1}{1999.2009}\)

\(=\frac{1}{10}\times\left(\frac{10}{9.19}+\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)

\(=\frac{1}{10}\times\left(\frac{1}{9}-\frac{1}{19}+\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(=\frac{1}{10}\times\left(\frac{1}{9}-\frac{1}{2009}\right)\)

\(=\frac{1}{10}\times\frac{2000}{18081}\)

\(=\frac{200}{18081}\)

_Chúc bạn học tốt_

Ta có:

\(\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\)

\(=\frac{1}{19}+9\left(\frac{1}{19.29}+\frac{1}{29.39}+...+\frac{1}{1999.2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)(Đây là dạng tổng đặc biệt bn nha)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(=\frac{1}{9}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)\)

\(=\frac{1}{9}+\frac{9}{10}.\frac{1990}{38171}\)

\(=\frac{1}{9}+\frac{1791}{38171}\)

\(=0,1580...\approx0,16\)

\(A=\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)\)

\(=\frac{1}{19}+\frac{1791}{38171}\)

\(=\frac{200}{2009}\)

Vậy \(A=\frac{200}{2009}\)

Ta có:

\(A=\dfrac{1}{19}+\dfrac{9}{19.29}+\dfrac{9}{29.39}+...+\) \(\dfrac{9}{1999.2009}\)

\(=\dfrac{1}{19}+\) \(\left(\dfrac{9}{19.29}+\dfrac{9}{29.39}+...+\dfrac{9}{1999.2009}\right)\)

\(=\dfrac{1}{19}\) \(+\) \(\dfrac{9}{10}\left(\dfrac{10}{19.29}+\dfrac{10}{29.39}+...+\dfrac{10}{1999.2009}\right)\)

\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{39}+...+\dfrac{1}{1999}-\dfrac{1}{2009}\right)\)

\(=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)=\dfrac{200}{2009}\)

Vậy \(A=\dfrac{200}{2009}\)

Ta có : \(A=\dfrac{1}{19}+\dfrac{9}{19.29}+\dfrac{9}{29.39}+...+\dfrac{9}{1999.2009}.\)\(\Rightarrow A=\dfrac{1}{19}+\left(\dfrac{9}{19.29}+\dfrac{9}{29.39}+...+\dfrac{9}{1999.2009}\right)\)\(\Rightarrow A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{10}{19.29}+\dfrac{10}{29.39}+..+\dfrac{10}{1999}+\dfrac{10}{2009}\right)\)\(\Rightarrow A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{39}+...+\dfrac{1}{1999}-\dfrac{1}{2009}\right)\)\(\Rightarrow A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)\)

\(\Rightarrow A=\dfrac{1}{19}+\dfrac{9}{10}.\dfrac{1990}{38171}\)

\(\Rightarrow A=\dfrac{1}{19}+\dfrac{1791}{38171}\)

\(\Rightarrow A=\dfrac{200}{2009}\)

Vậy \(A=\dfrac{200}{2009}\)

\(\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\)

= \(\frac{1}{19}+\left(\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\right)\)

= \(\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2009}\right)\)

= \(\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

= \(\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)\)

= \(\frac{1}{19}+\frac{9}{10}.\frac{1990}{38171}\)

= \(\frac{1}{19}+\frac{1791}{38171}\)

= \(\frac{200}{2009}\)

\(A=\frac{1}{19}+\frac{9}{10}\left(\frac{10}{19.29}+\frac{10}{29.39}+...+\frac{10}{1999.2000}\right)\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2000}\right)\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2000}\right)\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1990}{38171}\right)\)\(=\frac{1}{19}+\frac{1791}{38171}\)\(=\frac{200}{2009}\)

Nhớ k mik nha bạn Capricorn

200/209

mk ko bt 123

Ta có:

A=\(\frac{1}{19}\)+\(\frac{9}{19\cdot29}\)+\(\frac{9}{29\cdot39}\)+.......+\(\frac{9}{1999\cdot2009}\)

A=\(\frac{1}{19}\)+\(\frac{9}{10}\)\(\times\)(\(\frac{10}{19\cdot29}\)+\(\frac{10}{29\cdot39}\)+......+\(\frac{10}{1999\cdot2009}\))

A=\(\frac{1}{19}\)+\(\frac{9}{10}\)\(\times\)(\(\frac{1}{19}\)-\(\frac{1}{29}\)+\(\frac{1}{29}\)-\(\frac{1}{39}\)+.....+\(\frac{1}{1999}\)-\(\frac{1}{2009}\))

A=\(\frac{1}{19}\)+\(\frac{9}{10}\)\(\times\)(\(\frac{1}{19}\)-\(\frac{1}{2009}\))

A=\(\frac{200}{2009}\)

Vậy A=\(\frac{200}{2009}\)

Chúc bạn thi tốt! Đúng thì tick giúp mk nha!

link:https://hoc24.vn/hoi-dap/question/171569.html

mik lm rồi nhưng ko muốn viết lại nên bn chịu khó vào link nha!>.<!

là 200/2009 mình làm rồi

A = \(\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\)

\(=\frac{1}{19}+\left(\frac{9}{19.29}+\frac{9}{29.39}+...+\frac{9}{1999.2009}\right)\)

\(=\frac{1}{19}+9\left(\frac{1}{19.29}+\frac{1}{29.39}+...+\frac{1}{1999.2009}\right)\)

\(=\frac{1}{19}+9.\frac{1}{10}\left(\frac{1}{19}-\frac{1}{29}+\frac{1}{29}-\frac{1}{39}+...+\frac{1}{1999}-\frac{1}{2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}\left(\frac{1}{19}-\frac{1}{2009}\right)\)

\(=\frac{1}{19}+\frac{9}{10}.\frac{1990}{38171}\)

\(=\frac{1}{19}+\frac{1791}{38171}\)

\(=\frac{200}{2009}\)