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What ideas do you have to get it?
It is also not quite as simple as that either. What if you needed x^7's coefficient and the power was 1 000 000 000. Wolfram can not get that.
I understand, but this sort of thing will probably come up in either STEP I, II or III. It's usually the first question and they want you to do it 'systematically' -- which takes 15-25 minutes. But if I use a shortcut, it could take 2 minutes! In an exam where time is of the essence, those extra minutes could be a whole grade.
That is a different problem then the one we were working on back around #9500.
That is because that one is too short. To be on the safe side it should be at least:
Suppose we want the co-efficient of x^7 in:
Which one does it not work for? Do you have an example?
Yeah, that's what I wrote at the top of the page -- but it doesn't always seem to work...
I think I have it, I do not know how we got confused back then . Let's try again.
with k is the power, n is x^n. This should work fine.
Okay, thank you.
Sort of an emergency because STEP II is tomorrow morning...
then the co-efficient of x^n is
if n is less than or equal to the middle co-efficient (if it isn't, just use the opposite value of n, using the symmetry of the binomial expansion).
But trying this out on other examples, this doesn't seem to work and at best seems to be an approximation, getting weaker for higher powers. Do you know the correct closed form for the co-efficient of x^n in such an expansion?
Yes, but it is hard to barbecue them.
Looks like we are discussing cooking. I love fried eggs.
Very good! I cook the same but have not been able to barbecue for many years.