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DameLight
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Hello, I'm looking for some help with this problem for my Calculus 2 class. Since it's a summer class my professor wasn't able to explain everything fully so if you can help me that would be great : )
1. Homework Statement
Select the FIRST correct reason why the given series converges.
A. Convergent geometric series
B. Convergent p series
C. Comparison (or Limit Comparison) with a geometric or p series
D. Alternating Series Test
E. None of the above
1. Σn=1∞ 6(4)n/72n
2. Σn=1∞ sin2(6n)/n2
3. Σn=1∞ cos(nπ)/ln(2n)
4. Σn=1∞ (−1)n/(6n+5)
5. Σn=1∞ (n+1)(24)n/52n
6. Σn=1∞ (−1)n * √(n)/(n+9)
Geometric Series:
Σn=1∞ arn-1 will converge if -1 < r < 1
P Series:
Σn=1∞ 1/np converges if p > 1
Alternating Series Test:
1) bn+1 </= bn for all n and
2) limn->∞ bn = 0
1. A
2. B
3. E
4. D
5. C
6. D
1. Homework Statement
Select the FIRST correct reason why the given series converges.
A. Convergent geometric series
B. Convergent p series
C. Comparison (or Limit Comparison) with a geometric or p series
D. Alternating Series Test
E. None of the above
1. Σn=1∞ 6(4)n/72n
2. Σn=1∞ sin2(6n)/n2
3. Σn=1∞ cos(nπ)/ln(2n)
4. Σn=1∞ (−1)n/(6n+5)
5. Σn=1∞ (n+1)(24)n/52n
6. Σn=1∞ (−1)n * √(n)/(n+9)
Homework Equations
Geometric Series:
Σn=1∞ arn-1 will converge if -1 < r < 1
P Series:
Σn=1∞ 1/np converges if p > 1
Alternating Series Test:
1) bn+1 </= bn for all n and
2) limn->∞ bn = 0
The Attempt at a Solution
1. A
2. B
3. E
4. D
5. C
6. D
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