Question

Convergent or divergent?

Answer 1

Convergent

Explanation:

This is an alternating series where bn = 2n / eⁿ. Apply the alternating series test:

lim(n→∞) bn

= lim(n→∞) (2n / eⁿ)

Use L'hopital's rule:

= lim(n→∞) (2 / eⁿ)

= 0

For n ≥ 1, the series is decreasing. 2(n+1) / eⁿ⁺¹ < 2n / eⁿ.

Therefore, the series converges.