Using Substitution to Prove an Big O/upper bound is O(n^3)

I need to use a substitution method to prove and show that T(n) is in O(n³) for

$T(n) = 2T(\lfloor \frac{n}{2} \rfloor) + 5n^3 $ 

for n ? 2, T(1) = 20

I am supposed to come up with an explicit guess for the upper bound instead of trying to reason using order notation.



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  • It took me about 35 minutes to write this solution. You should offer higher amounts in future, otherwise your questions may not get answered.

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