subtomex0 subtomex0

30-05-2024
Mathematics

Answered

Is there any closed form for the following sum:
\(\displaystyle\sum_{k=0}^{n} \dfrac{(30-3x)^k}{(n-k)k!}\)

Verified Answer :

yuzhong885 yuzhong885

30-05-2024

Answer:

Yes, that's a binomial series. The closed form for this sum is \(\frac{1}{n!}(30-3x)^n e^{3x}\).

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