Prove that if ∑an converges absolutely, then both ∑Pn and ∑Nn converge

Prove that if ∑a_n converges absolutely, then both ∑P_n and ∑N_n converge

Expert Solution

If converges absolutely then series converges.

are positive terms of series

and are negative terms of series .

Since series and both converges.

Therefore, their sum also converges

=> also converges

=> converges

Similarly, as and converges.

Therefore, also converges

=> also converges.

=> converges.

Hnece, and converges if converges absolutely.

Colby Messinger answered 1 year ago

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Question

Prove that if ∑an converges absolutely, then both ∑Pn and ∑Nn converge

Solutions

Expert Solution

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