Question

[Duong Pham]

Tính nhanh:

A=\(\dfrac{1}{2.3}\) +\(\dfrac{1}{3.4}\) +\(\dfrac{1}{4.5}\) +....+\(\dfrac{1}{99.100}\).

B=\(\dfrac{3}{2.5}\) +\(\dfrac{3}{5.8}\)+\(\dfrac{3}{8.11}\)+....\(\dfrac{3}{92.95}\).

C=\(\dfrac{7}{1.3}\) +\(\dfrac{7}{3.5}\)+\(\dfrac{7}{5.7}\)+\(\dfrac{7}{7.9}\)+.....+\(\dfrac{7}{49.51}\)

Answer 1

[JakiNatsumi]

A = \(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

A=\(\dfrac{1}{2}-\dfrac{1}{100}=\dfrac{50}{100}-\dfrac{1}{100}=\dfrac{49}{100}\)

Answer 2

[JakiNatsumi]

B = \(\dfrac{3}{2.5}+\dfrac{3}{5.8}+\dfrac{3}{8.11}+...+\dfrac{3}{49.51}\)

B = \(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{49}-\dfrac{1}{51}\)

B = \(\dfrac{1}{2}-\dfrac{1}{51}=\dfrac{51}{102}-\dfrac{2}{102}=\dfrac{49}{102}\)