Examine the Two Series Below for Absolute Convergence (A), Convergence $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { ( n + 2 ) 3 ^ { n } } { 2 ^ { 2 n + 1 } }$

Multiple Choice

Examine the two series below for absolute convergence (A) , convergence that is not absolute (C) , or divergence (D) .
1) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { ( n + 2 ) 3 ^ { n } } { 2 ^ { 2 n + 1 } }$
2) $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { ( n + 3 ) 2 ^ { 2 n } } { 3 ^ { n + 100 } }$

A) 1A, 2A
B) 1A, 2C
C) 1A, 2D
D) 1C, 2A
E) 1C, 2C
F) 1C, 2D
G) 1D, 2A
H) 1D, 2C