Using the Ratio Test In Exercises 17-38, use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. ∑ n = 1 ∞ ( − 1 ) n [ 2 ⋅ 4 ⋅ 6 ⋯ ( 2 n ) ] 2 ⋅ 5 ⋅ 8 ⋯ ( 3 n + 1 )
Using the Ratio Test In Exercises 17-38, use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. ∑ n = 1 ∞ ( − 1 ) n [ 2 ⋅ 4 ⋅ 6 ⋯ ( 2 n ) ] 2 ⋅ 5 ⋅ 8 ⋯ ( 3 n + 1 )
Solution Summary: The author calculates whether the given series is convergent or divergent.
Using the Ratio Test In Exercises 17-38, use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
∑
n
=
1
∞
(
−
1
)
n
[
2
⋅
4
⋅
6
⋯
(
2
n
)
]
2
⋅
5
⋅
8
⋯
(
3
n
+
1
)
Proof In Exercises 17–20, prove that the Maclaurin series for the function converges to the function for all x.
Calc and Anal Geometry II
SHOW ALL WORK
Use the Ratio test to determine whether the series converges or diverge
∞
∑ (-1)n(2n+1)/n!
n=1
Mathmatics
determine whether the series converges, diverges to ±∞, or diverges, not to ±∞. If the series converges, find what it converges to.
A. ∑(1/√2n+2 - 1/√2n)
B.∑1 / ( n⋅(n+3) )
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