Section 5.5 « Difference Equations to Differential Equations

Section 5.5

By cssp

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1. (a) The series converges by the ratio test: $\rho = \dfrac{1}{2}$ .

(e) The series converges by the ratio test: $\rho = 0$ .

(g) The series converges by the ratio test: $\rho = 0$ .

(h) The series diverges by the ratio test: $\rho = \pi$ .

2. (a) The series diverges by the limit comparison test with a $p$ -series with $p = \dfrac{1}{2}$ .

(e) The series converges by the ratio test: $\rho = \dfrac{1}{4}$ .

(g) The series diverges by the $n$ th term test for divergence since

$\displaystyle{\lim_{n \to \infty}\frac{3n + 1}{2n - 1} = \frac{3}{2}}$ .

3. (a) $(-1, 1)$

4. (a) $(-\infty, \infty)$

5. The series converges by the ratio test since

$\displaystyle{\rho = \lim_{n \to \infty}\frac{a_{n+1}}{a_n} = \frac{1}{2}}$ .

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Difference Equations to Differential Equations

Section 5.5

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