Suppose that absolute value of (c) is less than 1 and that, for every positive integer n,
(X sub n) = the summation from i=1 to n, of c^(i-1)
Explain why,
(X sub n) approaches (1/(1-c))
Thanks for your help!!
It's the sum of a geometric series: $\displaystyle \sum^n_{i=0}r^i=\frac{1-r^{n+1}}{1-r}$ , so now you've to take the limit in both sides when $\displaystyle n\rightarrow \infty$ , and....what's the limit of $\displaystyle r^n\,,\,\,|r|<1$ ? Exactly!