Solution: Use partial fractions: $ \frac1k(k+2) = \frac12\left( \frac1k - \frac1k+2 \right) $. The sum becomes $ \frac12 \left( \sum_k=1^50 \frac1k - \sum_k=1^50 \frac1k+2 \right) = \frac12 \left( \sum_k=1^50 \frac1k - \sum_k=3^52 \frac1k \right) $. Telescoping gives $ \frac12 \left( \frac11 + \frac12 - \frac151 - \frac152 \right) = \frac12 \left( \frac32 - \frac1032652 \right) = \frac12 \cdot \frac39752652 = \frac13251768 $. \boxed\dfrac13251768 - Veritas Home Health