Thread: 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))

Thanks for your help!!

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))

Thanks for your help!!

It's the sum of a geometric series: , so now you've to take the limit in both sides when , and....what's the limit of ? Exactly!

Tonio