1. ## Monotone Sequences

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))

2. Originally Posted by Slazenger3
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))

It's the sum of a geometric series: $\sum^n_{i=0}r^i=\frac{1-r^{n+1}}{1-r}$ , so now you've to take the limit in both sides when $n\rightarrow \infty$ , and....what's the limit of $r^n\,,\,\,|r|<1$ ? Exactly!

Tonio