## Algebra 2 (1st Edition)

$\qquad \displaystyle \sum_{n=1}^{\infty}\frac{n^{2}}{n^{2}+1}$
From the first four terms, we observe the pattern nth numerator = $n^{2}$ nth denominator = (numerator)+1 = $n^{2}+1$ So, the nth term is $\displaystyle \frac{n^{2}}{n^{2}+1}.$ The first term corresponds to n=1 (lower limit). The sum has infinitely many terms (no upper limit ... we write $\infty$) Summation notation:$\qquad \displaystyle \sum_{n=1}^{\infty}\frac{n^{2}}{n^{2}+1}$