Question

A=\(\frac{1}{2.3}+\frac{1}{3.4}+\cdots+\frac{1}{\left(2n-1\right).2n}\)

Answer 1

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\cdots+\frac{1}{\left(2n-1\right)2n}\)

\(A=\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{2n-1}-\frac{1}{2n}\)

\(A=\frac12-\frac{1}{2n}\)

\(A=\frac{n}{2n}-\frac{1}{2n}=\frac{n-1}{2n}\)

Vậy \(A=\frac{n-1}{2n}\)

Answer 2

`A = 1/(2.3) + 1/(3.4) + ... + 1/((2n-1).2n)`

`A = 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/(2n-1) - 1/(2n) `

`A = 1/2 - 1/(2n) `

`A = (n-1)/(2n)`