Brownian Motion Converges to Std Normal

Purpose
If you take a symmetrical random walk and scale it, it becomes a browninan motion.

> par(mfrow = c(1, 1))
> library(ConvergenceConcepts)
> genTnL <- function(n) {
+     delta <- 1/n
+     ds <- sqrt(delta) * rnorm(n)
+     S <- cumsum(ds)
+     Z <- S/(sqrt(delta) * sqrt(n))
+     return(Z)
+ }
> plot(genTnL(10000), type = "l")

The above clearly shows that as you increase sample paths, the scaled brownian motion converges to a standard normal.