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# Infinite series order of terms watch

1. Q: http://gyazo.com/5d4e59735c8f7bf2b1591119fb0e335e

note: there is a hint in the question saying to consider the terms with even and odd indicies seperately

I'm having troubles getting started with this question:

Does the question want me to find a general formula for and then prove that using the root test or use and prove that using the root test?

Any help on getting started - thanks
2. (Original post by TDL)
Q: http://gyazo.com/5d4e59735c8f7bf2b1591119fb0e335e

note: there is a hint in the question saying to consider the terms with even and odd indicies seperately

I'm having troubles getting started with this question:

Does the question want me to find a general formula for and then prove that using the root test or use and prove that using the root test?

Any help on getting started - thanks
The odd and even terms form two separate geometric series. Does that help?
3. I would think you're supposed to apply the root test directly to the given series. Note that the n^th term is K/2^n where K = 1/2 or 2; once you take nth roots the value of K isn't going to matter for large n.
4. (Original post by brianeverit)
The odd and even terms form two separate geometric series. Does that help?
It does but, are we allowed to just split up a_n like that? Is that not rearranging it again? I.e. can we say ?

(Original post by DFranklin)
I would think you're supposed to apply the root test directly to the given series. Note that the n^th term is K/2^n where K = 1/2 or 2; once you take nth roots the value of K isn't going to matter for large n.
Thanks that worked well for part a), however that doesn't work so well for part b: http://gyazo.com/97547384a1ac8f51553737bcc8898094

we have and
and we can't necessarily conclude that is less than 2 if K can equal 2

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