Question

[Thầy Đức Anh]

(0,5 điểm)Tính:

$\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\ldots+\dfrac{2}{99.101}$

Answer 1

[Nguyễn Thị Thương Hoài]

A = \(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + ...........+ \(\dfrac{2}{99.101}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) +............+ \(\dfrac{1}{99}\) - \(\dfrac{1}{101}\)

A = \(\dfrac{1}{1}\) - \(\dfrac{1}{101}\)

A = \(\dfrac{100}{101}\)

Answer 2

[Minh An]

A=21.3+23.5+25.7+...+299.101=1−13+13−15+15−17+...+199−1101=1−1101=100101