Infinite series Knowledge-Based Download PDF

Questions

1. 1.

   For what values of the real constant $p$ does the infinite series $\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^p}$ converge?

   • A) $p \ge 1$
   • B) $p > 0$
   • C) $p > 1$
   • D) $p < 1$
2. 2.

   Which of the following statements is true regarding the convergence of the series $\sum_{n=1}^{\infty} \frac{(-1)^n}{\sqrt{n} + 1}$?

   • A) The series converges absolutely.
   • B) The series diverges by the Divergence Test.
   • C) The series converges conditionally.
   • D) The series diverges by the Limit Comparison Test.
3. 3.

   What is the interval of convergence of the power series $\sum_{n=1}^{\infty} \frac{(x - 3)^n}{n 2^n}$?

   • A) $(1, 5)$
   • B) $[1, 5]$
   • C) $[1, 5)$
   • D) $(1, 5]$
4. 4.

   What is the sum of the infinite series $\sum_{n=1}^{\infty} 5\left(-\frac{3}{4}\right)^n$?

   • A) $\frac{20}{7}$
   • B) $-\frac{20}{7}$
   • C) $\frac{15}{7}$
   • D) $-\frac{15}{7}$
5. 5.

   What is the sum of the infinite series $\sum_{n=1}^{\infty} \frac{2}{n(n+2)}$?

   • A) 1
   • B) 2
   • C) $\frac{4}{3}$
   • D) $\frac{3}{2}$