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sammii2u

  • 3 years ago

Do the following series converge?

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  1. sammii2u
    • 3 years ago
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    \[\sum_{n=1}^{\infty} \frac{ e^{-\sqrt{n}} }{ \sqrt{n} }\] \[\sum_{n=2}^{\infty} \frac{ 1 }{ n(\ln n)^3 }\]

  2. geerky42
    • 3 years ago
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    I don't do this thing yet so I may be wrong... Ask yourself a question. Which increase faster as n approaches to infinity? \(\large e^{-\sqrt{n}}\) or \(\sqrt{n}\). If \(\large e^{-\sqrt{n}}\) increase faster or approach to something greater than \(\sqrt{n}\), then it diverges. Otherwise it converges. What does \(n(\ln n )^3\) approach to when n approach to infinity? If it approaches to something under one, then it diverges, otherwise it converges.

  3. amoodarya
    • 3 years ago
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    for the first use ratio test that is converegent and for the second use integral test see what i draw|dw:1360527817600:dw| that is also conv

  4. sammii2u
    • 3 years ago
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    Thank you!

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