Question

[Lê Vũ Kim Ngân]

A=1/3x5 + 1/5x7 +1/7x9 +.....+1/97x99
Giups con với ạ

Answer 1

[Nguyễn Thị Thương Hoài]

A = \(\dfrac{1}{3\times5}\) + \(\dfrac{1}{5\times7}\) + \(\dfrac{1}{7\times9}\) + ... + \(\dfrac{1}{97\times99}\)

A = \(\dfrac{1}{2}\) x (\(\dfrac{2}{3\times5}\) + \(\dfrac{2}{5\times7}\) + \(\dfrac{2}{7\times9}\) + ... + \(\dfrac{2}{97\times99}\))

A = \(\dfrac{1}{2}\) x (\(\dfrac{1}{3}-\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}-\dfrac{1}{9}\) + ... + \(\dfrac{1}{97}\) - \(\dfrac{1}{99}\))

A = \(\dfrac{1}{2}\) x ( \(\dfrac{1}{3}\) - \(\dfrac{1}{99}\))

A  = \(\dfrac{1}{2}\times\left(\dfrac{33}{99}-\dfrac{1}{99}\right)\)

A = \(\dfrac{1}{2}\times\dfrac{32}{99}\)

A = \(\dfrac{16}{99}\)