let $ a $ real number and let $u_{n}=n^a$, let p a positive integer larger then $a$, help me to prove that the limit of $ (\Delta^p)_n= \sum_{i=0}^p (-1)^{p-i}\binom {p} {i}u_{n+i}$ is $0$ when n goes to infinity, $\Delta$ is the euler transform defined by : $ \Delta(u)_{n}= u_{n+1}-u_{n}$ and $\Delta^p=\Delta o\Delta^{p-1}$ Thank you very much
computing a limit
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analysis
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0but n^a isn't a polynomial – 2011-06-30
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0I accidentally read it as 'a' being a positive integer, and deleted my comment after realizing my error. Sorry about that. – 2011-06-30