Monday, 13 August 2018

sequences and series - Convergence using Root Test

Problem: test if the series convergesn=1(2)n+1nn+1



My approach:



I see it is equal to n=1(2)nnn2n, and n=1(2)nnn converges absolutely using root test, and n=12n diverges by using p-series test.



So is the original series divergent because convergent * divergent = divergent?




Is convergent * convergent = convergent??

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