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Math Help - [SOLVED] Series (p-series)

  1. #1
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    [SOLVED] Series (p-series)

    if my an = 1 / (n+1)^2
    can i use p series test to confirm that the series will converge..
    where p = 2..
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  2. #2
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    no it wont work. the p series test only works when the denominator is n raised to a power 1/n or 1/n^2 or 1/n^(3/2)

    even when you indirectly use the p series test with direct comparison or limit comparison an must still be in the form of 1/n

    the integral test works the integral 1/(x+1)^2 ,x,0,infinity converges thus the series converges ... the sum however is not found that way.
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  3. #3
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    ok..so.. what test should i use to know whethere it is convergence or divergence?
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  4. #4
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    Quote Originally Posted by nameck View Post
    if my an = 1 / (n+1)^2
    can i use p series test to confirm that the series will converge..where p = 2..
    Quote Originally Posted by osolage View Post
    no it wont work. the p series test only works when the denominator is n raised to a power 1/n or 1/n^2 or 1/n^(3/2)
    Well of course it works. One just has to understand the process.
    \sum\limits_{n = 1}^\infty  {\frac{1}{{\left( {n + 1} \right)^2 }}}  = \sum\limits_{k = 2}^\infty  {\frac{1}{{\left( k \right)^2 }}}
    The series on the right is a convergent p-series.

    Of notice that \frac{1}{(n+1)^2}\le \frac{1}{n^2} use comparison test.
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  5. #5
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    polar to cartesian

    deleted mssg
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