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categoryرياضيات
schoolبكالوريوس
event_available2026-07-14
السؤال
Transcribed Image Text:
an
Suppose that an > 0 and bn > 0 for n ≥N (N an integer). If lim
= ∞ and Σan converges, can anything be said about
b
n-∞
n
Σb? Give reasons for your answer.
Choose the correct answer below.
A. Nothing can be said about the series Σ bn. The Limit Comparison Test, in this case, does not mention anything about
Σb being convergent or divergent when Σan converges.
○ B.
n
The series Σb is a divergent series. By the Limit Comparison Test, since lim = ∞ and and a converges,
then Σb diverges.
noo
an
○ C.
The series Σb is a convergent series. By the Limit Comparison Test, since lim
= ∞ and and an
bn
noo
converges, then Σb converges.
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