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n=1

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n=2

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n=3

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n=4

By now you should be noticing the pattern.

Lets look at the numerator:

the leading term is always 2n-1 and it skips every other number. so we can write it like this:

And of course you notice that this n=4 and that this really means the numerator is

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And now we look at the denominator

And we notice that the leading term is always 2n. So we evaluate it a bit.

And of course you notice that n=4 and that this holds for any iteration. So the denominator becomes

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Then you consolidate the function for the numerator and denominator