Question

[Đinh bùi tiến đạt]

1/1.2+1/2.3+1/3.4+...1/100.101

Answer 1

[titanic]

Áp dụng \(\frac{1}{a.\left(a+1\right)}=\frac{1}{a}-\frac{1}{a+1}\)

Ta có \(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{100.101}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{100}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

Answer 2

[Jungkook Oppa]

1/1.2+1/2.3+1/3.4+.....+1/100/101

=1-1/2+1/2-1/3+1/3-1/4+.....+1/100-1/101

=1-1/101

=100/101