Question

What is a sample summation notation problem?

Answer 1

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

These means the sum:

`S_n = 1 + 2 + 3 + 4 + ...`

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 =1/2n(n+1)`

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 = 1/2(6)(6+1) = (6xx7)/2 = 21`