Absolute Convergence vs Conditional Convergence vs Convergence
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- Опубліковано 7 жов 2024
- We've seen regular convergence of a series before, but now we consider two special cases. Absolute convergence is when we take the series of the absolute value of the terms, which gets rid of any possible cancellation like what happened a lot in the Alternating Series Test. Absolute convergence implies regular convergence. Conditional Convergence is when it converges but does not converge absolutely.
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Sir give me an answer is that, following series are absolutely convergent or conditionally convergent or divergent....
(a)1-(1/1!)+(1/2!)-(1/3!)+.....
(b)1-(1/3)+(1/5)-(1/7)+.....
(c)(1/2)-(2/3)+(3/4)-(4/5)+.....
(d)1-1+(1/2)-(1/2)+(1/3)-(1/3)+....
(e)1-(1/2)+(1/2)-(1/2²)+(1/3)-(1/2³)+(1/4)-(1/2⁴)+.....