Question

Tính nhanh

\(C=\frac{6}{3.5}+\frac{6}{5.7}+....+\frac{6}{45.47}\)

Note: . là dấu nhân

Giúp mình với, làm đầy đủ cách giải nhé

Answer 1

\(C=\frac{6}{3.5}+\frac{6}{5.7}+...+\frac{6}{45.47}\)

\(\Rightarrow C=\frac{6}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{45}-\frac{1}{47}\right)\)

\(\Rightarrow C=3.\left(\frac{1}{3}-\frac{1}{47}\right)\)

\(\Rightarrow C=3.\frac{44}{141}\)

\(\Rightarrow C=\frac{44}{47}\)

Answer 2

\(C=\frac{6}{3.5}+\frac{6}{5.7}+...+\frac{6}{45.47}=3.\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{45.47}\right)=3.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{45}-\frac{1}{47}\right)\\ \)

\(=3.\left(\frac{1}{3}-\frac{1}{47}\right)=\frac{3.44}{141}=\frac{44}{47}\)