Dear Colleagues,
I am back from a very -- very long vacation and have the following
problems I need some assistance:
Problem # 1:
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Consider the following expansions:
a). (1-n^-1)^n = e^-1(1-n^-1/2 - 5/24n^-2 + O(n^-3))
b). b/(n-1)^2 = b/n^2 + O(n^-3).
In (a) and (b) above, powers of order 3 and above have been truncated
or are negligible using big O - notation.
My question is: How does one determine the truncation point(e.g.
powers of order 3 and over being negligible as in (a) and (b) above ?
I need to know this reasoning /method .
Problem #2:
__________
What is meant by :
- an expression for a quantinty ,say , f(n) being in closed form?
- a closed form solution?
Hope to get informative replies.
Yours sincerely,
June Simakani
Department of Statistics
University of Trtanskei
Private Bag X1, Unitra
Umtata 5117, South Africa.
Tel.no: + 27(47)502 2529(work)
+ 27(47)532 6380(res)
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