Question

Tính:

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

Answer 1

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

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

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

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

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

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

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