Exercise 3.3

MA111: Prepared by Dr.Archara Pacheenburawana 51
(s) a n = cos2 n
2 n (t) a n = (1+3n) 1/n
(u) a n = 1 n + 2 2 n +···+ n (v) a 2 n 2
n = ncosn
n 2 +1
(w) a n = n!
(x) a
2 n n = (−3)n
n!
Answer to Selected Exercise 7.1
1. (a) 0.8,0.96,0.992,0.9984,0.99968 (c) −3, 3 2 ,−1, 1,− 1 (e) {1,0,−1,0,1,...}
2 8 40
2. (a) a n = 1/2 n (c) 5n−3 (e) ( − 2 3
) n−1
3. (a) D (c) 5 (e) 0 (g) 0 (i) D (k) 0 (m) 0 (o) 0 (q) 0 (s) 0 (u) 1 2
(w) D
Exercise 7.2
Determine whether the series is convergent or divergent. If it is convergent, find its sum.
1. 4+ 8 + 16 + 32 +··· 2. −2+ 5 − 25 + 125 −···
5 25 125 2 8 32
∞∑
3. 5 ( 2 n−1
∞∑ (−3)
3) n−1
4.
5.
7.
9.
11.
13.
15.
17.
n=1
∞∑
3 −n 8 n+1 6.
n=1
∞∑
n=1
∞∑
n=1
1
n(n+2)
n
√
1+n
2
8.
10.
∞∑
arctann 12.
n=1
∞∑ [ (
2
1
) n ( )
4 +3 −
1 n ]
5
n=1
14.
∞∑
( 1
n − 1 )
n−1
16.
∞∑ ( e
) n+1
π
18.
n=2
n=1
n=1
n=1
4 n
∞∑ n
n+5
∞∑
[2(0.1) n +(0.2) n ]
n=1
∞∑ 3 n +2 n
n=1
6 n
∞∑ n
ln
n+1
n=1
∞∑ n−5
n+2
n=1
∞∑ n!
100 n
n=1
∞∑
(
3
(n−1) − 3 )
2 n 2
n=2