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Math Help - sum of series convergence or divergence?

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    sum of series convergence or divergence?

    Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.


    i thought it was 0..that's wrong help please?

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    Quote Originally Posted by Jessica11 View Post
    Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.

    \sum\limits_{n = 1}^\infty  {\frac{{5^n  + 4^n }}<br />
{{20^n }}}  = \sum\limits_{n = 1}^\infty  {\frac{1}<br />
{{4^n }}}  + \sum\limits_{n = 1}^\infty  {\frac{1}<br />
{{5^n }}}
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    Quote Originally Posted by Jessica11 View Post
    Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.


    i thought it was 0..that's wrong help please?

    The terms of the series go to zero (that's one of the conditions for convergence), but their sum does not.
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    Quote Originally Posted by redsoxfan325 View Post
    The terms of the series go to zero (that's one of the conditions for convergence), but their sum does not.
    That's not necessarily true. The terms going to zero says nothing of the convergence or divergence of a series.
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    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by Danny View Post
    That's not necessarily true. The terms going to zero says nothing of the convergence or divergence of a series.
    I said that's one of the conditions. The terms have to go to zero for the series to converge, but obviously it alone doesn't imply convergence.
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    Quote Originally Posted by redsoxfan325 View Post
    I said that's one of the conditions. The terms have to go to zero for the series to converge, but obviously it alone doesn't imply convergence.
    I simply don't want people to think that the terms going to zero implies convergence! It was the way it was stated - those that don't know might find the implication.
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    Quote Originally Posted by Jessica11 View Post
    Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE.
    i thought it was 0..that's wrong help please?
    @ Danny & redsoxfan325
    What are you both talking about?
    There is nothing in that post about terms of the series converging to zero.
    The OP did think that the sum of the series is zero.
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    Quote Originally Posted by Plato View Post
    @ Danny & redsoxfan325
    What are you both talking about?
    There is nothing in that post about terms of the series converging to zero.
    The OP did think that the sum of the series is zero.
    My comment was not to the OP but for those reading this thread. I often see that student's think that terms going to zero imply convergence. I just wanted to re-iterate that that is not necessarily true - that's all.
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    so if it is convergent then how do I find the sum of it?
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    Quote Originally Posted by Plato View Post
    \sum\limits_{n = 1}^\infty {\frac{{5^n + 4^n }}<br />
{{20^n }}} = \sum\limits_{n = 1}^\infty {\frac{1}<br />
{{4^n }}} + \sum\limits_{n = 1}^\infty {\frac{1}<br />
{{5^n }}}
    Each is a geometric series that converges. Treat each separately, find the sum, the add.
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  11. #11
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    thank you!
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