Sy123
This too shall pass
- Joined
- Nov 6, 2011
- Messages
- 3,730
- Gender
- Male
- HSC
- 2013
Re: HSC 2013 4U Marathon
ii) It is obvious that one simply needs to pick the right function f(x), it is clear then that we need to find some function f so that:
This may not always give the correct answer, because it is possible the sum inside the limit may be manipulated or simplified further, but we can simply verify our result once we find a good guess as to what the function is.
We can verify this by simply putting 1+k/n back in.
So f(x) = 1/(1+x^2), the answer then is
ii) It is obvious that one simply needs to pick the right function f(x), it is clear then that we need to find some function f so that:
This may not always give the correct answer, because it is possible the sum inside the limit may be manipulated or simplified further, but we can simply verify our result once we find a good guess as to what the function is.
We can verify this by simply putting 1+k/n back in.
So f(x) = 1/(1+x^2), the answer then is
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