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Apr
24
comment Why is $\sum_{k=1}^\infty -n k^{n-1}=\sum_{k=1}^\infty \left(k^n-(k-1)^n\right)$?
@user1952009 still I do not see the answer to this question there. Btw, why the downvotes?
Apr
23
comment Why is $\sum_{k=1}^\infty -n k^{n-1}=\sum_{k=1}^\infty \left(k^n-(k-1)^n\right)$?
@user1952009 It would be great if there was a proof that these two series are actually equivalent on a higher level than just having coincided Ramanujan's sums. For instance, one can be shown to be able to be derived from the other using some elementary operations that are known to never affect the sum of any series.
Apr
23
comment Why is $\sum_{k=1}^\infty -n k^{n-1}=\sum_{k=1}^\infty \left(k^n-(k-1)^n\right)$?
@user1952009 The thing is I am thinking about a non-standard numerical system for whose elements I constructed two definitions, from totally diferrent considerations. On the both definitions I defined the operation of multiplication. The first one uses a geometric approach and sutable for any two non-st numbers, the second one uses zeta regularization and suitable for powers of one distinguished element. Here the right side represent the formulas from geometric definition, the left side represents the zeta approach. It seems they coincide.
Apr
23
comment Why is $\sum_{k=1}^\infty -n k^{n-1}=\sum_{k=1}^\infty \left(k^n-(k-1)^n\right)$?
@user1952009 I do not see examples on page 9.
Apr
23
comment Why is $\sum_{k=1}^\infty -n k^{n-1}=\sum_{k=1}^\infty \left(k^n-(k-1)^n\right)$?
@user1952009 ??
Apr
23
comment Why is $\sum_{k=1}^\infty -n k^{n-1}=\sum_{k=1}^\infty \left(k^n-(k-1)^n\right)$?
@user1952009 it is defined rigorously. en.wikipedia.org/wiki/Divergent_series
Apr
23
revised Why is $\sum_{k=1}^\infty -n k^{n-1}=\sum_{k=1}^\infty \left(k^n-(k-1)^n\right)$?
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Apr
23
comment Why is $\sum_{k=1}^\infty -n k^{n-1}=\sum_{k=1}^\infty \left(k^n-(k-1)^n\right)$?
@user1952009 what exactly?
Apr
23
asked Why is $\sum_{k=1}^\infty -n k^{n-1}=\sum_{k=1}^\infty \left(k^n-(k-1)^n\right)$?
Apr
18
awarded  Popular Question
Apr
11
revised Classifying countable sets of weighted dots on a real line.
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Apr
11
revised Classifying countable sets of weighted dots on a real line.
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Apr
11
revised Classifying countable sets of weighted dots on a real line.
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Apr
10
awarded  Nice Question
Mar
29
awarded  Good Question
Mar
22
revised Classifying countable sets of weighted dots on a real line.
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Mar
14
revised Classifying countable sets of weighted dots on a real line.
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Mar
14
revised Classifying countable sets of weighted dots on a real line.
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Mar
14
comment Classifying countable sets of weighted dots on a real line.
@Akiva Weinberger yes! And maybe better set of rules that would be simpler but include these all.
Mar
14
revised Classifying countable sets of weighted dots on a real line.
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