Final answer:
Using the Alternating Series Test, the series provided meets the conditions for convergence as the terms decrease in absolute value and tend to zero. Therefore, the alternating series converges.
Step-by-step explanation:
The student has asked whether the alternating series ∑ₙ=1[infinity](-1)ⁿ+1(n/17)ⁿ converges or diverges. To determine this, we can use the Alternating Series Test. This test requires that the series' terms decrease in absolute value to zero as n tends to infinity. For our series, considering the terms (n/17)ⁿ, we notice that as n increases, these terms will indeed decrease because the base (n/17) is less than 1 for all n ≥ 1. Additionally, the exponential part with n ensures that these terms approach zero.
For an alternating series like this, if the terms decrease in absolute value to zero, the series converges. Since this is the case with our series, we can confidently say that the given alternating series converges.