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anonymous

  • 5 years ago

how do prove divergence of this infinite alternating series; sum_(n=0)^\infty [1/(1-n^-4)]

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  1. anonymous
    • 5 years ago
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    \[\sum_{n=0}^{\infty} (1/(5-2/n^4 )\]

  2. anonymous
    • 5 years ago
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    this series

  3. anonymous
    • 5 years ago
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    For alternating series, the following series must satisfy the following conditions to be convergent , else it'll be divergent : 1) lim n --> infinity = 0 2) Series must be decreasing If it happens that the following series doesn't satisfy one of the conditions, then it's considered divergent. Another try is the kth-term test of divergence, you can simply take the limit of the following series and check, if the limit is "NOT" equal to zero then the series diverges, if the limit is = 0, then it's convergent ^_^ give it a try now, I hope this made things clear for you :)

  4. anonymous
    • 5 years ago
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    hmm I've tried the ratio test, and kth term test of div. without conclusion.. I thought the Leibniz test only holds for convergence, not divergence?

  5. anonymous
    • 5 years ago
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    never heard of leibniz test, try the AST

  6. anonymous
    • 5 years ago
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    ok, leibniz test is the same AST.. The AST gives me that sequence is decreasing, but the it's convergening towards 1/5, thus I cannot use the AST, right? can AST be used for proving divergence of series?

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