# Math Help - sigma notation

1. ## sigma notation

$\sum\limits_{k=1}^n {\left( {3k/n} \right)}$

Express the sums in closed form

2. Hello,
Originally Posted by vinson24
$\sum\limits_{k=1}^n {\left( {3k/n} \right)}$

Express the sums in closed form
Note that the "variable" within the sum is k.

So you can take out n and 3 :

$\sum_{k=1}^n \frac{3k}{n}=\frac 3n \sum_{k=1}^n k$

$\sum_{k=1}^n k=\frac{n(n+1)}{2}$ (it's a known sum)

Hence $\sum_{k=1}^n \frac{3k}{n}=\frac 3n \times \frac{n(n+1)}{2}=\frac{3(n+1)}{2}$

3. thanks thats alot easier than the book shows it