Mathegoras

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Sum of fractions with shared denominators

Elementary school · ●●○○○ 20 pts

Find the value of (12+13+⋯+120)+(23+⋯+220)+⋯+(1819+1820)+1920\left(\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{20}\right)+\left(\frac{2}{3}+\cdots+\frac{2}{20}\right)+\cdots+\left(\frac{18}{19}+\frac{18}{20}\right)+\frac{19}{20}.

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fractionsarithmetic seriesGauss sumdistributive property