I have the following assignment:
Prove that $\sum^n_{i=1} i2^i \in \Theta(n2^n)$
My current approach thus far is the following:
Since we need to prove $k_1 \cdot n2^n \le \sum^n_{i=1} i2^i \le k_2 n2^n$ I chose $k_1 = 1$ and $k_2 = 2$. This holds true to my condition. However I'm unsure whether I can just freely decide on using those two.
Therefore my question is:
Am I allowed to chose any constant factor I want in a $\Theta$ proof (given that the condition holds true)?