Determining Convergence or Divergence In Exercises 27-34, test for convergence or divergence, using each test at least once. Identity which test was used. (a) nth-Term Test (b) Geometric Series Test (c) p-Series Test (d) Telescoping Series Test (e) Integral Test (f) Direct Comparison Test (g) Limit Comparison Test ∑ n = 1 ∞ n ( n 2 + 1 ) 2
Determining Convergence or Divergence In Exercises 27-34, test for convergence or divergence, using each test at least once. Identity which test was used. (a) nth-Term Test (b) Geometric Series Test (c) p-Series Test (d) Telescoping Series Test (e) Integral Test (f) Direct Comparison Test (g) Limit Comparison Test ∑ n = 1 ∞ n ( n 2 + 1 ) 2
Solution Summary: The author explains that the given series converges by the use of the integral test.
Determining Convergence or Divergence In Exercises 27-34, test for convergence or divergence, using each test at least once. Identity which test was used.
(a) nth-Term Test
(b) Geometric Series Test
(c) p-Series Test
(d) Telescoping Series Test
(e) Integral Test
(f) Direct Comparison Test
(g) Limit Comparison Test
∑
n
=
1
∞
n
(
n
2
+
1
)
2
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
1
Σ
In which case is the convergence test that should be used to determine the
character of the series and the result to be reached correctly?
n. Inn
n=2
(a) Integral Test is used; series is convergent
(b) Integral Test is used; series is divergent
(c) E
Comparison (Direct Comparison) Test is performed with the series, the series
n° is convergent
n=2
(d)
Comparison (Direct Comparison) Test is performed with the series; series is
3
n=2
divergent
(e) The Ratio Test is used; series is convergent
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