Question

1/1.2+1/2.3+1/3.4+...+1/110.111 =?

Answer 1

CHO TOG TRÊN LÀ A

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{110.111}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{110}-\frac{1}{111}\)

\(=1-\frac{1}{111}\)

\(=\frac{110}{111}\)