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1. https://www8.imperial.ac.uk/content/...1P1/m1p1s2.pdf

I need help on question 5.

We can write r = 1+x. Then we have (1+x)^n >= 1+nx i.e.
r^n >= 1 + rn - n

But how does this help us?

Also, would the following argument work?

r^n = exp(n*log r).
log r is clearly negative because of our value of r. So now it's obvious (and we should be able to prove it using the series expansion of exp) that as n goes to infinity, this goes to zero.
2. You don't write , that's impossible for a positive number x. Instead, what can you do with to make it less than one, like r?

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so let (you can rearrange to define x specifically if you want).
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Finally:
By 4(b) goes to 0
3. In regard to the post above, I think it's more natural to "do something to r to make it greater than 1", so to speak.

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1/r > 1, so 1/r = (1+x) for some x > 0. Then use 4b.

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