talpajocotefnf3

2022-03-26

Consider the following sequences.

a) Find the first four terms of the sequence.

b) Based on part (a), determine a plausible limit of the sequence.

${a}_{n}=\frac{{n}^{2}}{{n}^{2}-1};n=2,3,4,\dots$

a) Find the first four terms of the sequence.

b) Based on part (a), determine a plausible limit of the sequence.

Eve Larson

Beginner2022-03-27Added 9 answers

1)Given:

${a}_{n}=\frac{{n}^{2}}{{n}^{2}-1};n=2,3,4,\dots$

Put$n=2$

$a}_{2}=\frac{{2}^{2}}{{2}^{2}-1}=\frac{4}{3$

Put$n=3$

$a}_{3}=\frac{{3}^{2}}{{3}^{2}-1}=\frac{9}{8$

Put$n=4$

$a}_{4}=\frac{{4}^{2}}{{4}^{2}-1}=\frac{16}{15$

Put$n=5$

$a}_{5}=\frac{{5}^{2}}{{5}^{2}-1}=\frac{25}{24$

Thus, first four terms:$\frac{4}{3},\frac{9}{8},\frac{16}{15},\frac{25}{24}$

2) As the value of n increases, the value of$a}_{n$ approaches to 1. Therefore, the limit of the sequence is 1.

Put

Put

Put

Put

Thus, first four terms:

2) As the value of n increases, the value of

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