# Math Help - sigma notation

1. ## sigma notation

Find $\sum_{r=4}^{n}(lg3^{r})$

what i did was:

$=(lg 3) \sum_{r=4}^{n}(r)$
$=(lg 3)(\frac{1}{2})(n^{2}+7n)$

i used $\frac{n}{2}[2a+(n-1)d]$ to expand $\sum_{r=4}^{n}(r)$

but the suggested answer is $(lg 3)(\frac{1}{2})(n-3)(n+4)$........
where did i go wrong?

2. The sum has n-3 terms, not n terms.

3. Originally Posted by red_dog
The sum has n-3 terms, not n terms.
then...
$\frac{n-3}{2}[2(4)+((n-3)+1)]$
=(1/2)(n-3)(n+6)

....i still don't get the (n+4)....@"@

4. Originally Posted by wintersoltice
then...
$\frac{n-3}{2}[2(4)+((n-3)+1)]$
=(1/2)(n-3)(n+6)

....i still don't get the (n+4)....@"@
$\frac{n-3}{2}[2\cdot 4+(n-3-1)]=\frac{(n-3)(n+4)}{2}$