Since each term of the series is 1.1 times the previous one, the series is geometric. The generic term of a geometric series is
[tex]a_{n}=a_{0}\cdot r^{(n-1)}[/tex]
The sum in sigma notation simply adds these terms. The leading factor of 100 can be factored out.
[tex]sum=\displayform{100\cdot\sum\limits_{n=1}^{20}{1.1^{(n-1)}}}[/tex]
The sum can be found by adding the terms or by using the formula for the sum of a geometric series. In the latter case, we have
[tex]sum=100\cdot\dfrac{1.1^{20}-1}{1.1-1}\approx5727.50[/tex]
The series is divergent because the common ratio of terms is greater than 1. (Of course, any finite number of terms will have a finite sum.)
