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1. Consider the series \(\sum_{n = 1}^{\infty} \frac{n^2 + n + 3}{2n^2 + 10 n}\)

a.  The series converges by the \(n\)th term test.

b.  The series diverges by the \(n\)th term test.

c.  The series converges by the integral test.

d.  The series diverges by the integral test.

2. Consider the series \(\sum_{n = 2}^{\infty} \frac{1}{n\ln n}\)

a.  The series converges by the \(n\)th term test.

b.  The series diverges by the \(n\)th term test.

c.  The series converges by the integral test.

d.  The series diverges by the integral test.

3. Consider the series \(\sum_{n = 1}^{\infty} \frac{3^n}{4^n - 1}\)

a.  The series converges by the \(n\)th term test.

b.  The series diverges by the \(n\)th term test.

c.  The series converges by the LCT.

d.  The series diverges by the LCT.

4. Consider the series \(\sum_{n = 1}^{\infty} (-1)^{n+1} \frac{n}{n+1}\)

a.  The series converges by the \(n\)th term test.

b.  The series diverges by the \(n\)th term test.

c.  The series converges by the integral test.

d.  The series converges by the LCT.

5. Find the limit of the series \(\sum_{n = 1}^{\infty} \frac{9}{2}(\frac{1}{10})^n\)

a.  \(\frac{9}{10}\)

b.  \(4.75\)

c.  \(5\)

d.  \(\frac{11}{2}\)

e.  This series diverges.