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Svetllana [295]
4 years ago
10

Convergent or divergent?

Mathematics
1 answer:
navik [9.2K]4 years ago
6 0

Answer:

Convergent

Step-by-step 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.

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