It's a summation (sigma) notation.
[tex]\sum\limits_{i=1}^n a_i = a_1 + a_2 + ... a_n\\[/tex]
This expression means the sum of all the terms [tex]a_i[/tex], where i takes the values from 1 to n.
So i is the index (like a counter) and n is the last value.
In this case:
[tex]\sum\limits_{n=1}^6\frac{n}{2n+1} =\frac{1}{2*1+1}+ \frac{2}{2*2+1}+ \frac{3}{2*3+1}+ \frac{4}{2*4+1}+ \frac{5}{2*5+1}+ \frac{6}{2*6+1} \\= \frac{1}{3}+ \frac{2}{5}+\frac{3}{7}+\frac{4}{9}+\frac{5}{11}+\frac{6}{13}=\frac{113623}{45045} \approx 2.522\\\\[/tex]
