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Determine the value of p for the p-series given below.
[infinity]
∑ 3n²⋅n1/3
n=1

User Voyager
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Final answer:

The student's question relates to finding the value of p in a p-series. By simplifying the series expression 3n^2 ⋅ n^{1/3}, the value of p is determined to be 7/3, which indicates that the series converges as p is greater than 1.

Step-by-step explanation:

The student has asked to determine the value of p for a p-series sum. The notation for the series is not standard, however, it seems clear that the student is being asked about a series of the form ∑_{n=1}^{∞} 3n^2 ⋅ n^{1/3}. To find the value of p in a p-series, it essentially refers to the exponent in the term n^p where p is a positive constant. For convergence of a p-series, the value of p must be greater than 1.

Here, by simplifying the given expression, we obtain 3n^2 ⋅ n^{1/3} = 3n^{2 + 1/3} = 3n^{7/3}. The series therefore is a p-series with p = 7/3, which is greater than 1, indicating the series converges.

User Zefiro
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