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!!

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- Mar 25th 2010, 03:51 PMSlazenger3Monotone 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))

Thanks for your help!! - Mar 25th 2010, 04:08 PMtonio

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!(Wink)

Tonio