5. $S=(\frac{2}{7}+(\frac{2}{7})^2+(\frac{2}{7})^3+...)+(\frac{4}{7}+(\frac{4}{7})^2+(\frac{4}{7})^3+...)+(\frac{6}{7}+(\frac{6}{7} )^2+(\frac{6}{7})^3+...)=\frac{\frac{2}{7}}{1-\frac{2}{7}}+\frac{\frac{4}{7}}{1-\frac{4}{7}}+\frac{\frac{6}{7}}{1-\frac{6}{7}}=\frac{2}{5}+\frac{4}{3}+6$
ดังนั้น $15S=6+20+90=116$
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