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Math Help - methods on determining convergence or divergence

  1. #1
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    methods on determining convergence or divergence

    Can you use either taking the limit or solve the integral to find out if \sum_{n=1}^\infty\frac{n}{\sqrt{n^2+1}} diverges or converges?
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    Quote Originally Posted by Possible actuary View Post
    Can you use either taking the limit or solve the integral to find out if \sum_{n=1}^\infty\frac{n}{\sqrt{n^2+1}} diverges or converges?
    the limit test for divergence is the easiest method.

    \lim_{n \to \infty} \frac {n}{ \sqrt {n^2 + 1}} \neq 0 thus the series diverges
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    Quote Originally Posted by Possible actuary View Post
    Can you use either taking the limit or solve the integral to find out if \sum_{n=1}^\infty\frac{n}{\sqrt{n^2+1}} diverges or converges?
    The problem becomes harder if we consider \sum_{n=1}^\infty\frac{n}{\sqrt{n^3+1}} or \sum_{n=1}^\infty\frac{n}{\sqrt{n^4+1}}
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