Concrete Mathematics, problem 2.31
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Evaluating two sums with Riemann
Evaluating two sums with Riemann zeta function. We exchange the order of summation by Tonelli’s theorem, use partial fraction decomposition and telescope a bunch of terms. Results turn out to be quite nice! This problem was stated in great many a place, in particular in 𝐶𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝑀𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑠 textbook, problem 31 from the 2nd chapter.
Source: R. L. Graham, D. E. Knuth, O. Patashnik, 𝐶𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝑀𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑠. 𝐴 𝑓𝑜𝑢𝑛𝑑𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟 𝑠𝑐𝑖𝑒𝑛𝑐𝑒 (2nd ed.), Addison-Wesley Professional, 1994.
Source: R. L. Graham, D. E. Knuth, O. Patashnik, 𝐶𝑜𝑛𝑐𝑟𝑒𝑡𝑒 𝑀𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑠. 𝐴 𝑓𝑜𝑢𝑛𝑑𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟 𝑠𝑐𝑖𝑒𝑛𝑐𝑒 (2nd ed.), Addison-Wesley Professional, 1994.
7 ماه پیش
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