# How do you use summation notation to expression the sum  5+15+45+...+3645?

Mar 5, 2017

$5 + 15 + 45 + \ldots + 3645 = {\sum}_{r = 0}^{6} \setminus {3}^{r} \cdot 5 = 5 \setminus {\sum}_{r = 0}^{6} \setminus {3}^{r}$

#### Explanation:

Let the given summation be denoted by $S$

Then:

$S = 5 + 15 + 45 + \ldots + 3645$
$\setminus \setminus \setminus = 5 + 3 \cdot 5 + 9 \cdot 5 + \ldots + 729 \cdot 5$
$\setminus \setminus \setminus = {3}^{0} \cdot 5 + {3}^{1} \cdot 5 + {3}^{2} \cdot 5 + \ldots + {3}^{6} \cdot 5$
$\setminus \setminus \setminus = {\sum}_{r = 0}^{6} \setminus {3}^{r} \cdot 5$
$\setminus \setminus \setminus = 5 \setminus {\sum}_{r = 0}^{6} \setminus {3}^{r}$