MissMathsxo
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Hello,
I have to prove that 1/4n(n+1)-1/2 is order exactly n^2
I thought that it would be bounded order at most for big n^2 for all n>=1 but in this case how could it have an order at least. Is my order at most wrong? Thank you
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mqb2766
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(Original post by MissMathsxo)
Hello,
I have to prove that 1/4n(n+1)-1/2 is order exactly n^2
I thought that it would be bounded order at most for big n^2 for all n>=1 but in this case how could it have an order at least. Is my order at most wrong? Thank you
Do you have an image of the question?
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MissMathsxo
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(Original post by mqb2766)
Do you have an image of the question?
This is all my teacher gave me Name:  6F6685B5-6FFB-4BA8-933E-0755BA7C96C6.jpg.jpeg
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Size:  14.4 KB
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mqb2766
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(Original post by MissMathsxo)
This is all my teacher gave me Name:  6F6685B5-6FFB-4BA8-933E-0755BA7C96C6.jpg.jpeg
Views: 19
Size:  14.4 KB
Not sure what the E(n) means and I'm presuming the O(n^2) is the big O notation.
In this context, it really just means that C(n) is a quadratic. For large n, when n doubles then C(n) will quadruple.
Simply expand C(n) into the usual n^2, n, constant terms and make the argument that the quadratic is dominant term.
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MissMathsxo
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(Original post by mqb2766)
Not sure what the E(n) means and I'm presuming the O(n^2) is the big O notation.
In this context, it really just means that C(n) is a quadratic. For large n, when n doubles then C(n) will quadruple.
Simply expand C(n) into the usual n^2, n, constant terms and make the argument that the quadratic is dominant term.
Sorry, I think they're both meant I be C(n). And the big symbol means both big o and omega so I need to shown that it can be less then or equal depending on the coefficient on n^2
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mqb2766
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(Original post by MissMathsxo)
Sorry, I think they're both meant I be C(n). And the big symbol means both big o and omega so I need to shown that it can be less then or equal depending on the coefficient on n^2
In the image is it
Theta(n^2)
or
O(n^2)
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MissMathsxo
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(Original post by mqb2766)
In the image is it
Theta(n^2)
or
O(n^2)
Theta
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mqb2766
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(Original post by MissMathsxo)
Theta
Ok, so you need to show that there is both a
* quadratic upper bound: c*n^2 for n>n0
and a
* quadratic lower bound: d*n^2 for n>n0
Have a go at doing either / both and if you have problems just post? Some examples at
http://www-cgrl.cs.mcgill.ca/~godfri...-Functions.pdf
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MissMathsxo
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(Original post by mqb2766)
Ok, so you need to show that there is both a
* quadratic upper bound: c*n^2 for n>n0
and a
* quadratic lower bound: d*n^2 for n>n0
Have a go at doing either / both and if you have problems just post? Some examples at
http://www-cgrl.cs.mcgill.ca/~godfri...-Functions.pdf
Oh, I have just realised why I was confused. I thought that the values you referred to as c and d had to be integers but they don't. Thank you for your response 😊
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