Mth 126 ‐01 Sec 8.1,2 Name: ________________________ Date: __ Solve the problems in the space provided. Show your work in order to receive credit. Each problem is worth 3 points. 1 – 3 Determine whether the sequence converges or diverges. If it converges, find the limit. 1) an = cos(2/n) 2) {arctan2n} (hint: A graph might help here) 3) an =
n
1+ n
4 a) Determine whether the sequence an =
2n − 3
is increasing, decreasing, or not monotonic. 3n + 4
4 b) Is the sequence bounded? Give a reason for your answer. 5, 6 Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 5) 1 + 0.4 + 0.16 + 0.064 + ∙∙∙ ( −6)n −1
∑
n −1
n =1 5
∞
6)