Question

[Trần Khánh Linh]

A=3/1.3+3/3.5+3/5.7+...+3/99.101

giúp mk vs

Answer 1

[nguyentruongan]

mk có 3 cáh mn xem cáh nào hen

\(A=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-......+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{3}{2}\left(1-\frac{1}{101}\right)\)

\(=\frac{100}{101}.\frac{3}{2}=\frac{105}{101}\)

c2 nhé

\(A=3\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.......+\frac{1}{99}-\frac{1}{101}\right)\)

\(A=3\left(1-\frac{1}{101}\right)=3.\frac{100}{101}=\frac{300}{101}\)

Answer 2

[Bùi Thị Ngọc Ánh]

\(A=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{99.101}\)

\(3A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\)

\(3A=\frac{1}{1}-\frac{3}{101}\)\(\Rightarrow A=\left(1-\frac{1}{101}\right):3=\frac{100}{303}\)