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7 Ιουν 2022 · Here is the proof of Ramanujan infinite series of sum of all natural numbers. This is also called as the Ramanujan Paradox and Ramanujan Summation. In this video you will also learn about...
Example: geometric series with increasing terms 1 + 2 + 4 + 8 +... = -1 Divergent series Borel summation: Can give a value to harder series but still agrees with previous methods. Loses a...
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1 Ιουλ 2024 · Ramanujan's Sum. The sum. (1) where runs through the residues relatively prime to , which is important in the representation of numbers by the sums of squares. If (i.e., and ' are relatively prime ), then. (2)
30 Απρ 2016 · I wanted to know how the Ramanujan series works only using basic calculus. Why is it a shocking fact for the sum of an infinite series to be $-\frac1{12}$? How is it important to us and how does it change our perspective towards mathematics?
the denominator of Bn contains each of the factors 2 and 3 once and only once, 2n(2n − 1)Bn. /. n is an integer and 2 (2n − 1)Bn consequently is an odd integer. In his 17-page paper "Some Properties of Bernoulli's Numbers" (1911), Ramanujan gave three proofs, two corollaries and three conjectures. [61]
17 Μαρ 2023 · Ramanujan sums. Trigonometric sums depending on two integer parameters $ k $ and $ n $: $$ c _ {k} ( n) = \sum _ { h } \mathop {\rm exp} \left ( \frac {2 \pi n h i } {k} \right ) = \ \sum _ { h } \cos \frac {2 \pi n h } {k} , $$. when $ h $ runs over all non-negative integers less than $ k $ and relatively prime to $ k $.
