Suppose we have a sequence [math]\left\{f_n\right\}[/math] with [math]n\in\mathbb{N}[/math], whose terms [math]f_1,f_2,f_3,\ldots[/math] are real numbers. For each [math]n\in\mathbb{N}[/math], we define the partial sum[br][center][math]S_n=f_1+f_2+\cdots+f_n[/math][/center][justify]of the first [math]n[/math] terms of [math]\left\{f_n\right\}[/math]. Thus we obtain a new sequence [math]\left\{S_n\right\}[/math], with [math]n\in\mathbb{N}[/math]. The following simulation shows the approximate values of the partial sums [math]\left\{S_n\right\}[/math], from 1 to 1000 terms.[br][br][b]Things to try:[/b][/justify][list][*]Drag the slider [b]n[/b] to explore the values of [math]S_n[/math].[/*][*]Change the function that define the series. [/*][*][b]Example:[/b] (-1)^(n+1)/n [/*][*][b]Example:[/b] n*sin(sqrt(n+1)) [/*][/list]