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Jan
18
comment $\lim_{{n}\to{\infty}} (n+1)!(e-1-{1\over2}-…-{1\over n!})= ?$
Is Cesaro-Stolz needed here ? The result is quite direct knowing that $a_n = \frac1{(n + 1)!}$ at leading order.
Dec
21
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Oct
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awarded  Nice Answer
Oct
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Sep
24
awarded  Autobiographer
Aug
24
comment Limit of differences of truncated series and integrals give Euler-gamma, zeta and logs. Why?
Note that you are looking at a particular case of Euler-Maclaurin formula: en.wikipedia.org/wiki/Euler%E2%80%93Maclaurin_formula
Aug
5
awarded  Teacher
Aug
5
answered In calculus, which questions can the naive ask that the learned cannot answer?
Aug
5
comment In calculus, which questions can the naive ask that the learned cannot answer?
As a (negative) application, the Risch algorithm, which is supposed to decide whether a function admits a closed-form antiderivative (and computes it if it exsts), cannot decide in general exactly because of this. The proof of its termination relies on one being able to tell whether a given expression is zero.
Aug
5
comment In calculus, which questions can the naive ask that the learned cannot answer?
@MichaelHardy: Your operator is nothing more than the Euler-Maclaurin series :)
Jan
25
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