Question

1. 1 Determine the monotonicity and bounded ness of each of the following sequences: 1 (i) \{a_n = \frac{1}{2n+3}\} 3^n (iv) \{a_n = \frac{3^n}{n!}\} (ii) \{a_n = \cos(\pi n)\} (v) \{a_n = \frac{n+1}{n+3}\} 3^n (iii) \{a_n = \} 2. Determine if each of the following sequences converges or diverges. If converges, find the limit: (i) $a_n = \{(1 + \frac{5}{n})^n\};$ 2n-3 (ii) \{a_n = \frac{2n-3}{3n+4}\} (iii) $\sqrt{n} - \sqrt{n+1}$ 3. Determine if each of the following series converges or diverges. If converges find the limit: $\sum_{1}^{\infty} \frac{n+1}{n+3}$ $\sum_{1}^{\infty} \frac{1}{2n+3}$ $\sum_{1}^{\infty} \frac{1}{3^n}$ $\sum_{1}^{\infty} \frac{2}{(n+2)(n+3)}$

          1. 1 Determine the monotonicity and bounded ness of each of the following
sequences:
1
(i) \{a_n = \frac{1}{2n+3}\}
3^n
(iv) \{a_n = \frac{3^n}{n!}\}
(ii) \{a_n = \cos(\pi n)\}
(v) \{a_n = \frac{n+1}{n+3}\}
3^n
(iii) \{a_n = \}
2. Determine if each of the following sequences converges or diverges. If
converges, find the limit:
(i) $a_n = \{(1 + \frac{5}{n})^n\};$
2n-3
(ii) \{a_n = \frac{2n-3}{3n+4}\}
(iii) $\sqrt{n} - \sqrt{n+1}$
3. Determine if each of the following series converges or diverges. If converges find
the limit:
$\sum_{1}^{\infty} \frac{n+1}{n+3}$
$\sum_{1}^{\infty} \frac{1}{2n+3}$
$\sum_{1}^{\infty} \frac{1}{3^n}$
$\sum_{1}^{\infty} \frac{2}{(n+2)(n+3)}$

$1. 1 Determine the monotonicity and bounded ness of each of the following sequences: 1 (i) {an = (1)/(2n+3)} 3^n (iv) {an = (3^n)/(n!)} (ii) {an = cos(πn)} (v) {an = (n+1)/(n+3)} 3^n (iii) {an = } 2. Determine if each of the following sequences converges or diverges. If converges, find the limit: (i) an = {(1 + (5)/(n))^n}; 2n-3 (ii) {an = (2n-3)/(3n+4)} (iii) √(n) - √(n+1) 3. Determine if each of the following series converges or diverges. If converges find the limit: ∑1^∞(n+1)/(n+3) ∑1^∞(1)/(2n+3) ∑1^∞(1)/(3^n) ∑1^∞(2)/((n+2)(n+3))$

Added by Michael R.

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