Question

Use the ratio test to show that the series is convergent. Thank you!

Answer 1

Step-by-step explanation:

lim(n→∞) |aₙ₊₁ / aₙ|

lim(n→∞) | (4ⁿ⁺¹ / (n+1)!) / (4ⁿ / n!) |

lim(n→∞) | (4ⁿ⁺¹ / (n+1)!) × (n! / 4ⁿ) |

lim(n→∞) | 4 / (n+1) |

0

Since the limit is less than 1, the series converges.