Question

Determine whether the sequence converges or diverges. If it converges, find the value it converges to.

aₙ = (-1)^(n-1) * n / (n² + 1)

Answer 1

The sequence converges to 0.

Step-by-step explanation:

To determine whether the sequence converges or diverges, we can examine the behavior of the terms as n approaches infinity. First, let's simplify the expression: aₙ = (-1)^(n-1) * n / (n² + 1). As n increases, the numerator (-1)^(n-1) * n oscillates between positive and negative values. The denominator (n² + 1) grows much faster than the numerator. So, as n goes to infinity, the terms of the sequence approach zero.

Therefore, the sequence converges to 0.