14. Sequences & Series

13–52. Limits of sequences

Find the limit of the following sequences or determine that the sequence diverges.

{(n + 1)!⁄n!}

13–52. Limits of sequences

Find the limit of the following sequences or determine that the sequence diverges.

{tan⁻¹(n)}

Limits of sequences

Find the limit of the following sequences or determine that the sequence diverges.

{nsin(6 / n)}

55–70. More sequences

Find the limit of the following sequences or determine that the sequence diverges.

aₙ = (−1)ⁿ ⁿ√n

55–70. More sequences

Find the limit of the following sequences or determine that the sequence diverges.

{nsin³(nπ / 2) / (n + 1)}"

55–70. More sequences

Find the limit of the following sequences or determine that the sequence diverges.

aₙ = e⁻ⁿcosn

55–70. More sequences

Find the limit of the following sequences or determine that the sequence diverges.

{tan⁻¹n / n}

55–70. More sequences

Find the limit of the following sequences or determine that the sequence diverges.

{cosn / n}

55–70. More sequences

Find the limit of the following sequences or determine that the sequence diverges.

{sinn / 2ⁿ}

55–70. More sequences

Find the limit of the following sequences or determine that the sequence diverges.

{(75n⁻¹ / 99ⁿ) + (5ⁿsinn / 8ⁿ)}

13–52. Limits of sequences

Find the limit of the following sequences or determine that the sequence diverges.

{√(n² + 1) − n} 

13–52. Limits of sequences

Find the limit of the following sequences or determine that the sequence diverges.

{(1 + (2 / n))ⁿ}

13–52. Limits of sequences

Find the limit of the following sequences or determine that the sequence diverges.

{ⁿ√(e³ⁿ⁺⁴)} 

Growth rates of sequences

Use Theorem 10.6 to find the limit of the following sequences or state that they diverge.

{n¹⁰ / ln20n}

Growth rates of sequences

Use Theorem 10.6 to find the limit of the following sequences or state that they diverge.

{n¹⁰⁰⁰ / 2ⁿ}