Having problems with big oh, Omega, theta Show the following:
$\ $ (a) $\, \sum_{i=1}^n(3i+2n)\text{ is }O(n^2)$
$\ $ (b) $\, \sum_{k=1}^n(k/3)\text{ is }\Omega(n^2)$
$\ $ (c) $\, \sum_{j=1}^n\sum_{k=1}^n 7n\text{ is }\Theta(n^3)$.
Thank you.

The first sum can be separated, giving you $2n(n)+\sum_1^n 3i$, which gives you $2n^2+\frac32(n+1)n$. Clearly this is $\mathcal{O}(n^2)$. The rest are similarly straightforward.
Use the definitions.
