True or false: if a n </msub> is any decreasing sequence of positive real number

velinariojepvg

velinariojepvg

Answered question

2022-05-09

True or false: if a n is any decreasing sequence of positive real numbers and b n is any sequence of real numbers converges to 0, then a n b n diverges.

Answer & Explanation

Maeve Holloway

Maeve Holloway

Beginner2022-05-10Added 25 answers

if a n = e n and b n = 1 n 2 then
( a n ) is a decreasing sequence of positive numbers and lim + b n = 0
but
a n b n = n 2 e n 0.
Jaeden Weaver

Jaeden Weaver

Beginner2022-05-11Added 4 answers

Hint: Take a n = b n = 1 n

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