# How do you use summation notation to expression the sum 7+14+28+...+896?

Feb 16, 2017

${\sum}_{r = 0}^{127} \setminus 7 + 7 r \setminus \setminus$ or $\setminus \setminus {\sum}_{r = 1}^{128} 7 r$

#### Explanation:

Let $S = 7 + 14 + 28 + \ldots + 896$

The first term is $7$, and we get subsequent terms by adding $7$ each time, so the series is:

$S = 7 + \left(7 + 7\right) + \left(7 + 2 \left(7\right)\right) + \left(7 + 3 \left(7\right)\right) + \ldots 896$
$\setminus \setminus = 7 + \left(7 + 7\right) + \left(7 + 2 \left(7\right)\right) + \left(7 + 3 \left(7\right)\right) + \ldots \left(7 + \left(127\right) 7\right)$
$\setminus \setminus = {\sum}_{r = 0}^{127} \setminus 7 + 7 r$

Alternatively if you prefer the sum to start from $r = 1$ we could write:

$S = \left(0 + \left(1\right) 7\right) + \left(0 + \left(2\right) 7\right) + \left(0 + 3 \left(7\right)\right) + \left(0 + \left(128\right) 7\right)$
$\setminus \setminus = {\sum}_{r = 1}^{128} 7 r$

(NB the sum evaluates to $S = 57792$)