# What is a sample summation notation problem?

Jan 13, 2017

You could be asked to find the sum of the first n Natural numbers.

These means the sum:

${S}_{n} = 1 + 2 + 3 + 4 + \ldots$

We write this in shorthand summation notation as;

${\sum}_{r = 1}^{n} r$

Where $r$ is a "dummy" variable. And for this particular sum we can find the general formula which is:

${\sum}_{r = 1}^{n} r = \frac{1}{2} n \left(n + 1\right)$

So for example, If $n = 6$ Then:

${S}_{6} = {\sum}_{r = 1}^{6} r = 1 + 2 + 3 + 4 + 5 + 6$

We can determine by direct calculation that:

${S}_{6} = 21$

Or use the formula to get:

${S}_{6} = \frac{1}{2} \left(6\right) \left(6 + 1\right) = \frac{6 \times 7}{2} = 21$