FP1 Proof by induction

Stuck on part 3, I've tried and cant get to the final answer.
Could someone show me the algebra please!

Show us what you already have.

I've got as far as 2/(2k-1)+2
not sure where to go from there

Your conjecture is that $u_n = \frac{2}{2k-1}$, yeah?

So verify that works for $u_1$.

Then show that $\displaystyle u_{k+1} = \frac{\frac{2}{2k-1}}{1 + \frac{2}{2k-1}} = \frac{2}{2k-1 + 2} = \frac{2}{2(k+1) -1}$

and you're done... that's the same form of $u_k$ except it has $k+1$ in place of $k$ as we'd expect in an induction, so that's sorted.

Thanks Zacken! One thing I don't get is when you're showing n=k+1, why is Uk on top of the fraction. Is it because it says it in the question?

Yep. The question says that $u_{k+1} = \frac{u_k}{1 + u_k}$ so that's the relation you use.

You're a life saver!

You're a life saver!

Were you just self studying further maths because to do AS Further Maths in year 13, or just for fun, or were you doing Further Maths AS in year 12? XD


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Actually did further maths in year 12 Scraped an A somehow, I did M1 & M2 so the first year was slightly tricky.

Taking the hard way out... Haha, no problem. The fact that you got an A doing FP1, M1 and M2 is enough man... Lol
I can't believe I helped you on a question and now you destroying maths literally lol


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How about yourself, what subjects are you taking? I'm sure you can do the same with a little bit of effort

Let's hope so. I don't even know to be honest, I'm the most unorganised guy in the world lol. I still have to buy suits, new bag, new everything lol. Even decide my new A-level options because my sixth form can't let me do my A-level options because the timetables clash...


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That really sucks, perhaps you could self teach the subjects they wont let you choose. It's only the beginning of the year, you'll get into the hang of things and become more organised as time goes by!