\(\frac{5}{24}+\frac{5}{104}+\frac{5}{234}+\frac{5}{414}\)
\(=\frac{5}{3.8}+\frac{5}{8.13}+\frac{5}{13.18}+\frac{5}{18.23}\)
\(=\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+\frac{1}{18}-\frac{1}{23}\)
\(=\frac{1}{3}-\frac{1}{23}=\frac{20}{69}\)
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\(\frac{5}{24}+\frac{5}{104}+\frac{5}{234}+\frac{5}{414}\)
\(=\frac{5}{3.8}+\frac{5}{8.13}+\frac{5}{13.18}+\frac{5}{18.23}\)
\(=\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}+\frac{1}{18}-\frac{1}{23}\)
\(=\frac{1}{3}-\frac{1}{23}\)
\(=\frac{20}{69}\)