how do prove divergence of this infinite alternating series;

sum_(n=0)^\infty [1/(1-n^-4)]

Question

how do prove divergence of this infinite alternating series;

sum_(n=0)^\infty   [1/(1-n^-4)]

anonymous · Answer

$$\sum_{n=0}^{\infty} (1/(5-2/n^4 )$$

anonymous · Answer

this series

anonymous · Answer

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 :)

anonymous · Answer

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?

anonymous · Answer

never heard of leibniz test, try the AST

anonymous · Answer

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?