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Extension: Similarities of Infinite Series and Improper Integrals

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Problems 1

The harmonic series is ∑i=1∞1i=11+12+13+⋯\sum^\infty_{i=1}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdotsi=1∑∞i1=11+21+31+⋯ This happens to be a right Riemann sum of…