Question

Các bạn giúp mk, mk cần gấp!

\(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+......+\frac{4}{99\times101}\)

Answer 1

\(\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{99.101}\)

\(=2.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

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

\(=2.\frac{100}{101}=\frac{200}{101}\)

Answer 2

Đặt \(A=\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+..+\frac{4}{99.101}\)

\(A=2.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(A=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

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

\(A=\frac{2.100}{101}=\frac{200}{101}\)

Ủng hộ mk nha !!! ^_^

Answer 3

Ta gọi tổng trên là A

Ta có: A = 4/1x3+4/3x5 + 4/5x7+...+4/99x101

=>A x 2/4 = 2/1x3+2/3x5+2/5x7+...+2/99x101

               =1-1/2+1/2-1/3+1/3-1/4+....+1/99+1/101

               =1-1/101=100/101