Which of the following assertions is true for the given

Jaeden Frederick 2022-01-24 Answered
Which of the following assertions is true for the given sequences?
1)Double exponent: use braces to clarify converges
2){n+12n+3} diverges
3){1+2(1)n} diverges
4){nsin1n} converges
5)None of these
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Expert Answer

Rylee Marshall
Answered 2022-01-25 Author has 6 answers

True sequences:
2) n+12n+3 diverges
3) 1+2(1)n diverges
an=n+12n+3
Now, check convergence of n=0an
n=0n+12n+3
Apply series Divergence test
=diverges
Thus, n=0n+12n+3: diverges

This is a true sequence
3)an=1+2(1)n
Check the convergence of n=0an
n=01+2(1)n
Apply Divergence test
=diverges
Thus, n=0a1+2(1)n:÷ers. Thus, this is a true sequence.

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