Question

Bài tự hỏi tự làm 1 (Công thức tổng quát):

Rút gọn A=\(\dfrac{1}{1.2}\) \(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+...+\(\dfrac{1}{n.\left(n+1\right)}\)

Yêu cầu không command.

Answer 1

Ta có A = \(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+...+\(\dfrac{1}{n\left(n+1\right)}\)

A = 1 - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) +...+ \(\dfrac{1}{n}\) - \(\dfrac{1}{n+1}\)

A = 1 -(\(\dfrac{1}{2}\)-\(\dfrac{1}{2}\)) - (\(\dfrac{1}{3}\)-\(\dfrac{1}{3}\)) - ... - \(\dfrac{1}{n+1}\)

A = 1 - \(\dfrac{1}{n+1}\)

A = \(\dfrac{n+1}{n+1}\) - \(\dfrac{1}{n+1}\)

A = \(\dfrac{n+1-1}{n+1}\)

A = \(\dfrac{n}{n+1}\)

Answer 2

NHờ ai đó xóa giúp mình câu này với