PeroK's latest activity

Yes, if you play a game with ##m## white balls and ##n-1## black balls, then ##p(m, n-1)## is the probability that the first player wins...

That's not an answer. I think what they are looking for is a recursion based on ##m, n##. Let ##p(m, n)## be the probability the...

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Can you think of another way to tackle the problem? Using a common mathematical idea.

I think they want the probability that the first player wins. So, you still have some work to do. That said, it's not clear whether...

For ##X = 2## you also need that the game was not won on the first turn.

I’ve also seen it written: $$\int fg’ \,dx = fg - \int f’g \,dx$$ Maybe you could preface with ‘f and g are functions of x’ and save...

After the proposed u-substitution, the partial fractions step is trivial. In any case, it must be much simpler to do the u-substitution...

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What you've written isn't right at all. I understand what you are trying to do. I just don't see the point of making it look like a...

PS I don't understand why parts isn't taught this way. I never really got the point of that weird "uv" thing!

Parts is really the inverse product rule. Start with the product rule for differentiation: $$\frac{d}{dx}\big (f(x)g(x)\big ) =...

I thought the comment about initial terms vanishing was a maths/physics in joke, but there it is made real. Your method is a lot...

Integration by parts is valid for a definite integral. That allows you in this case to simplify the integral to a known standard form...

The equation I posted can be shown by induction on ##n##. What you stumbled on is an interesting idea for how to generalise the...