EDB β€” 238

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Theorem 29

[238] Let bn be a sequence for which

bnβ‰₯bn+1>0,limnβ†’βˆžbn=0,

then the series

βˆ‘n=0+∞(βˆ’1)nbn

is convergent; also, called β„“ the value of the series, letting

BN=βˆ‘n=0N(βˆ’1)nbn

the partial sums, we have that the sequence B2N is decreasing , the sequence B2N+1 is increasing, and both converge to β„“.

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  • convergence, of a series
  • Leibniz, test
  • test, Leibniz β€”
  • test, alternating series β€” , see Leibniz test
  • alternating series test , see Leibniz test
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