Question

tinh

1/1.2.3+1/2.3.4+....+1/99.100.101

Answer 1

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{99.100.101}\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{99.100}-\frac{1}{100.101}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{100.101}\right)=\frac{5049}{20200}\)

Answer 2

1/1.2.3+1/2.3.4+...+1/99.100.101

= 1/2 ( 1/1.2-1/2.3+1/2.3-1/3.4+...+1/99.100-1/100.101)

=1/2(1/1.2-1/.100.101)=5049/20200