HW 2, MA 1023
In exercise 1, find a defining formula an = f (n) for the sequence.
1.
1) − 4,−3,−2,−1,0,··· 2)1
9
,−
2
12
,
2
2
15
,−
2
3
18
,
2
4
21
,···
In exercise 2-6, determine the convergence or divergence of the sequences. If the sequence is convergent, find the limit.
2.
(1) an = 1 + (−1)n
(2) an =
n + 1
2n
1 −
1
n
3.
(1) an =
sin2
(2n + 1)
n
2
(2) an =
cos(2n + 3)
2
n
4.
(1) an =
n + (−1)n+1
2n
(2) an =
2n + 1
1 − 3
√
n
5.
(1) an =
ln(2n + 1)
√
n
(2) an = cos(2π +
1
n
2
)
6.
(1) an =
(−4)n
n!
(2) an = 2 + (1
2
)
2n
7. Determine if the geometric series converges or diverges. If the series converges, find
the value.
(1)X∞
n=1
(−1)n
4
n+1 (2) X∞
n=1
(−3)n
2
n
8. Find a formula for the n-th partial sume of the series and use it to determine if the
series converges or diverges. If a series converges, find its value.
(1)X∞
n=1
3
n
2
−
3
(n + 1)2
!
(2) X∞
n=1
√
n + 4 −
√
n + 3
