Question

[Snow Princess]

1. Chứng tỏ rằng:

a) \(\dfrac{1}{a.\left(a+1\right)}=\dfrac{1}{a}-\dfrac{1}{a+1}\)

b) \(\dfrac{m}{a.\left(a+m\right)}=\dfrac{1}{a}-\dfrac{1}{a+m}\)

2. Tính

a) \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)

b) \(\dfrac{5}{10.15}+\dfrac{5}{15.20}+...+\dfrac{5}{195.200}\)

c) \(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{96.98}\)

Answer 1

[Đinh Ngọc Ánh]

2

a. \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)

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

=\(\dfrac{1}{2}-\dfrac{1}{100}\)

=\(\dfrac{49}{100}\)