Does anyone know how to solve the below? I'm guessing that I need to use the Subtraction method or iteration but still I'm having a hard time with it.
$$T(n)=3T(n-1)+3^n\times n^2$$
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5Possible duplicate of Solving or approximating recurrence relations for sequences of numbers – Discrete lizard Jan 21 '18 at 11:21
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Exapnd the equation:
$$T(n) = 3(3T(n-2) + 3^{n-1}\times(n-1)^2) + 3^n\times n^2=$$ $$3^2T(n-2) + 3^n(n^2 + (n-1)^2)= \cdots = $$ $$3^n\sum_{i=1}^{n}i^2 = 3^n \times \frac{n(n+1)(2n+1)}{6} = \Theta(3^n\times n^3) $$
OmG
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i don't understand the second and the third lines. can you explain it in more details ? – OmerMichleviz Jan 21 '18 at 16:04
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i dont understand the ". . ." .the sigma...how did you notice it? whats going on there – OmerMichleviz Jan 21 '18 at 16:49
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