\(\frac{2}{10}+\frac{2}{40}+\frac{2}{88}+\frac{2}{154}+\frac{2}{238}=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)
\(=\frac{2}{3}\cdot\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\right)\)
\(=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{17}\right)\)
\(=\frac{2}{3}\cdot\left(\frac{1}{2}-\frac{1}{17}\right)\)
\(=\frac{2}{3}\cdot\frac{15}{34}=\frac{2.15}{3.34}=\frac{1.5}{1.17}=\frac{5}{17}\)
Chú ý nè: Dấu "." là dấu "x" đó!
\(\frac{2}{10}+\frac{2}{40}+\frac{2}{88}+\frac{2}{154}+\frac{2}{238}=\frac{1}{4}+\frac{2}{88}+\frac{2}{154}+\frac{2}{238}=\frac{3}{11}+\frac{2}{154}+\frac{2}{238}=\frac{2}{7}+\frac{2}{238}=\frac{5}{17}\)
2/10+2/40+2/88+2/154+2/238
=1/5+1/20+1/44+1/77+1/119
=(1/5+1,20)+(1/44+1/77)+1/119
=1/10 + 1/111 +1/199
= 121/111 +1/119
=14510/13209
