Question

Tính 1/1.3+1/3.5+1/3.7+........+1/101.103

Answer 1

A = \(\dfrac{1}{1.3}\) + \(\dfrac{1}{3.5}\) + \(\dfrac{1}{5.7}\) + ... + \(\dfrac{1}{101.103}\)

A = \(\dfrac{1}{2}\).(\(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + ... + \(\dfrac{2}{101.103}\))

A = \(\dfrac{1}{2}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + ... + \(\dfrac{1}{101}\) - \(\dfrac{1}{103}\))

A = \(\dfrac{1}{2}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{103}\))

A = \(\dfrac{1}{2}\). \(\dfrac{102}{103}\)

A = \(\dfrac{51}{103}\)

Answer 2

Em ơi thừa số thứ ba phải là \(\dfrac{1}{5.7}\) mới đúng em nhé.