Question

[Phùng Khánh]

tinh nhanh 

A = 1/(1+2) + 1/(1+2+3).....+ 1/(1+2+3+4+5+6+7+8+9+10)

Answer 1

[tth_new]

\(A=\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+..+10}\)

\(=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{55}\)

\(=2\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=2.\left(\frac{1}{2}-\frac{1}{11}\right)=2.\frac{9}{22}=\frac{9}{11}\)