I need some help on this reduction formulae question.
The question is:
I know that the reduction formulae is
But I don't know how manipulate it into the above form. Could someone help please?
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
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
Then you consolidate the function for the numerator and denominator
When I become a cyborg, I won't forget things like this.