Question

Tính tổng các phân số sau

 

a       C=1/3×4+1/4×5+1/5×6+...............+1/101×102

Answer 1

\(C=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{101.102}\)

\(\Rightarrow C=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{101}-\frac{1}{102}\)

\(\Rightarrow C=\frac{1}{3}-\frac{1}{102}\)

\(\Rightarrow C=\frac{34}{102}-\frac{1}{102}=\frac{33}{102}=\frac{11}{34}\)

Answer 2

\(C=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+..+\frac{1}{101}-\frac{1}{102}\)

\(C=\frac{1}{3}-\frac{1}{102}\)

\(C=\frac{11}{34}\)