LIST 1
1. Compute sum of the first 10 terms of the arithmetic sequence (an ), when:
a) a1 = 3, a4 − a2 = 8, b) a5 = 4, a8 = 2, c) S5 = 30, a6 = 12
2. Compute sum of the first 8 terms of the geometric sequence (an ), when:
a) a2 = 2, a3 = 6, b) a3 = 2, a6 = 8
3. Verify if the following sequences are monotonic:
√
−3n+1
a) an = 2n − 8, b)an = n2 − 2n − 3, c)an = n+2
, e) n + 5
n+1 , d)an = 2
4.Compute limits of the following sequences:
2
+n
n8
−n2 +1
n+2
, b) an = 3n
, c)an = 20n+9
a) an = 2n+3
n3 +1 , d)an = 8n7 +4 , e) an = 2n2 +n
q 4n2 −4
n
4n3 +6
f) an = 3n+sin
n+2 , g)
9n3 −7
5.Compute limits of the following sequences:
n
3n +n
10×2n+3
52n−1
a) an = 2n2+8 , b) an = 2×3
n −1 , c)an =
6n −5 , d)an = 2×7n +9 , e) an =
√
√
3×8n+1
4n
n + 5 − n + 8,
f) an = 1+2+3+...+n
, g) an = 1+3+9+...+3
n , h) an =
23n −6 , √
√3n2
i) an = n2 + 2n − n2 + n
6.Compute limits of the following sequences, if they exist:
3
n
(−1)n ×2n+6
×sin n
cos n
n
, d) an = n +(−1)
a) an = 2 sin
n , b) an = n2 +1 , c) an =
n+8
5n3 +cos n
1