8.3. Series Without Negative Terms http://www.ck12.org
- Write an example of a sequence that is not nondecreasing.
- Suppose{Sn}is a nondecreasing sequence such that for eachM>0, there is anN, such thatSn> M for all
n>N. Does the sequence converge? Explain. - Determine if
{ 5 n 2
2 n^2 + 7}
converges or diverges. If it converges, find its limit.- Determine if∑∞k= 3 (^14 )k−^1 converges or diverges. If it converges, find its sum.
Determine if each series converges or diverges.
6.∑∞k= (^1) ( 4 k+^11 ) (^12)
7.∑∞k= (^13) k (^52) − 4
8.∑∞k= (^1) (k+ 1 )(^5 k+ 3 )
9.∑∞k= 1 √ (^57) k 2
10.∑k∞= 1 k 33 k+ (^64) +k 22 +k 41
11.∑∞k= (^1) ( 3 k−^11 ) (^52)
12. Maria uses the integral test to determine if∑∞k= (^1) k^32 converges. She finds that
+∫∞
1
x^32 =3. She then states that
∑∞k= (^1) k^32 converges and the sum is 3. What error did she make?
Keywords
- nondecreasing sequence
- harmonic series
- geometric series
- p−series
- Comparison Test
- Integral Test
- Limit Comparison Test
- Simplified Limit Comparison Test