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Math Help - can anyone give me two more examples?

  1. #1
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    can anyone give me two more examples?

    I am struggling to understand infinte series can anyone give me two more examples?
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  2. #2
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    Quote Originally Posted by jameyt View Post
    I am struggling to understand infinte series can anyone give me two more examples?
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  3. #3
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    How about this one:

    \sum_{n=1}^\infty 1-(\frac{1}{n})^\frac{1}{n}

    which diverges and can be seen defining the function:

    f(x) = 1-(\frac{1}{x})^\frac{1}{x} - \frac{1}{x}

    for x > 10, and seeing that it is always positive which would mean

    \frac{1}{n} is a lower bound ( when n is bigger than 10).

    but :

    \sum_{n=1}^\infty (-1)^n (1-(\frac{1}{n})^\frac{1}{n})

    converges due to Leibniz criteria.
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