iCoachMath.com: Examples on The Ratio and Root Tests - Infinite Series

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f Use the ratio test to determine whether the series ∑n=1∞ n3(n+1)! is convergent or divergent.
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f Use the ratio test to determine whether the series ∑ 1.2.3...n3.5.7...(2n+1) is convergent or divergent. f

f Use the ratio test to determine whether the series ∑ 3nn!nn is convergent or divergent.
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f Use the ratio test to determine whether the series ∑n=1∞ n2(2n-1)! is convergent or divergent. f

f Use Root Test to determine whether the series ∑n=1∞ nn31+2n is convergent or divergent.
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f Use the ratio test to determine whether the series ∑ n22n is convergent or divergent. f

f Determine the values of x for which the series converges absolutely.
1 + x + x22!+x33! + ... f

f Use the ratio test to determine whether the series ∑n=1∞ (-10)n42n+1(n+1) is convergent or divergent.
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f Use Root Test to determine whether the series ∑n=1∞ (- 1)²ⁿ (2 + 1n)ⁿ is convergent or divergent. f

f Use Root Test to determine whether the series ∑n=1∞ ( 1 + 1n)ⁿ 3^{- n} is convergent or divergent. f

f Which of the following is true for the series?
1 - 13 + 132-133 + ... f

f Use Root Test to determine whether the series ∑n=0∞ (5n-3n37n3+2)ⁿ is convergent or divergent. f

f Which of the following is true for the series?
1 + 123-133-143+153+163 - ... f

f Which of the following is true for the series?
∑n=1∞ xn(2n)! f

f Which of the following is true for the series?
∑n=1∞ (- 1)^{n + 1} nn2+1 f

f Which of the following is true for the series?
1 - 12+13-14 + ... f

f Which of the following is true for the series?
1 - 12+ 13- 14+ ... f

f Which of the following is true for the series?
∑n=1∞ cos nπn3 f

f Determine the values of x for which the series ∑n=1∞ (x+6)nn155n converges absolutely. f

f Use Root Test to determine whether the series ∑n=1∞ (-12)nn is convergent or divergent. f

f Use the ratio test to determine whether the series ∑n=1∞ (2n-1)!3n is convergent or divergent.
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f Determine the value of x for which the series ∑n=1∞ xn2n+1 converges conditionally.
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