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k_{n}=\frac{1}{2}+\frac{1}{13}
Reduce the fraction \frac{4}{52} to lowest terms by extracting and canceling out 4.
k_{n}=\frac{13}{26}+\frac{2}{26}
Least common multiple of 2 and 13 is 26. Convert \frac{1}{2} and \frac{1}{13} to fractions with denominator 26.
k_{n}=\frac{13+2}{26}
Since \frac{13}{26} and \frac{2}{26} have the same denominator, add them by adding their numerators.
k_{n}=\frac{15}{26}
Add 13 and 2 to get 15.