total value

[faik mermer]

How can I find the sum.Does it have formula?

 

[Dr.Peterson]

Looks like a geometric series to me.

 

[pka]

You need to find the value of \(\sum\limits_{k = 1}^{13} {{{\left( {\frac{6}{5}} \right)}^{2k}}} \). See Here
As noted above that is a finite geometric series.

 

[HallsofIvy]

Yes, that is (almost) a geometric series, \(\displaystyle \sum_{n=0}^\infty p^n\) with \(\displaystyle p= \left(\frac{4}{5}\right)^2= \frac{16}{25}\). The sum of such a geometric series, with |p|< 1, which it is here, is \(\displaystyle \frac{1}{1- p}\).

(I say "almost" because the first term of a geometric series is 1 but that is missing here. So subtract 1 from what you get from the formula above.)

(pka seems to think that is \(\displaystyle \frac{6}{5}\) rather than \(\displaystyle \frac{4}{5}\). That is the problem with hand written questions.)