(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the monotonicity of the sequence with An as indicated

An = (-1)^(2n+1) * n^0.5

3. The attempt at a solution

well without even doing any tests, I can see that 2n+1 is always odd, so the -1 will make every term negative

so it simplifies to

An = - root(n)

which is obviously a decreasing sequence.....

Now here is where my problem somes in

If i do a ratio test of An+1 / An I get

An+1 / An = [ (-1)^(2(n+1)+1) * root (n+1) ] / [ (-1)^(2n+1) * root (n) ]

= [ (-1)^(2n + 3) * root (n+1) ] / [ (-1)^(2n+1) * root (n) ]

when i divide (-1)^(2n + 3) by [ (-1)^(2n+1) i get (-1) ^ 2 which is 1

so An+1 / An reduces to = root (n+1) / root (n) which is always greater than 1.... now if its greater than one, doesn't it mean that each term is greater than th last, and the seqence is increasing? but from simplifying the expression for the term An I can clearly see that it hs to be decreasing...so where am I screwing up? Am i not supposed to apply ratio tests to sequences with each term being negative? or does the ratio test work the opposite way with sequences that are always negative (ie i need it to be less than one for it to be increasing and more than 1 for it to be decreasing?) This is probably a really dumb question.

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# Homework Help: What am I doing wrong? (Monotonicity of sequence)

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