Determine whether the series summationdisplay n 1 a n converges or diverges 1

# Determine whether the series summationdisplay n 1 a n

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Determine whether the series summationdisplay n =1 a n converges or diverges. 1. converges 2. diverges 3. neither converges nor diverges 008 10.0points Which one of the following properties does the series summationdisplay n =3 ( - 1) n 4 n (ln n ) n have? 1. absolutely convergent 2. conditionally convergent 3. divergent 009 10.0points Find all integers m > 1 for which both of the infinite series summationdisplay n =1 ( - 1) mn 2 n + 6 , summationdisplay n =1 parenleftBig m 11 parenrightBig n converge. 1. m = 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 2. m = 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 3. m = 3 , 5 , 7 , 9 4. m = 2 , 4 , 6 , 8 , 10 5. m = 3 , 5 , 7 , 9 , 11
fernando (rf9447) – HW03 – kalahurka – (55295) 3 010 10.0points Decide whether the series summationdisplay n =1 11 n parenleftBig n - 2 n parenrightBig n 2 converges or diverges. 1. converges 2. diverges 011 10.0points Which one of the following properties does the series summationdisplay n =1 parenleftbigg 4 - 3 n 2 4 + 5 n 2 parenrightbigg n have? 1. divergent 2. absolutely convergent 3. conditionally convergent 012 10.0points Determine whether the series summationdisplay n =0 ( - 8) n (2 n )! is absolutely convergent, conditionally con- vergent, or divergent. 1. divergent 2. absolutely convergent 3. conditionally convergent 013 10.0points To apply the ratio test to the infinite series summationdisplay n a n , the value of λ = lim n → ∞ a n +1 a n has to be determined. Compute λ for the series summationdisplay n =1 ( n !) 2 (2 n )! parenleftbigg 2 3 parenrightbigg n . 1. λ = 2 3 2. λ = 1 3 3. λ = 4 3 4. λ = 2 9 5. λ = 1 6 014 10.0points Which one of the following properties does the series 1 - 1 · 3 3! + 1 · 3 · 5 5! - 1 · 3 · 5 · 7 7! + . . . + ( - 1) n 1 · 3 · · · · (2 n - 1) (2 n - 1)! + . . . . have? 1. absolutely convergent 2. conditionally convergent 3. divergent 015 10.0points To apply the root test to an infinite series summationdisplay n a n the value of ρ = lim n → ∞ ( a n ) 1 /n
fernando (rf9447) – HW03 – kalahurka – (55295) 4 has to be determined.

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• Fall '07
• Fakhreddine/Lyon
• Mathematical Series, Radius of convergence