Post by A-gineSuppose {a_k} is a decreasing sequence of real number.
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Prove that if �U a_k converges, then k(a_k) �� 0 as k �� ��
k=1
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�U a_k converges ==> a_k �� 0
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2n
(2n)a_{2n} �� 2 �U a_k �� 0 as n����, by Cauchy criterion
k=n+1
2n-1
(2n-1)a_{2n-1} �� 2 �U a_k + a_{2n-1} �� 0
k=n
�G�o�� k(a_k) �� 0 as k �� ��.
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