Another sequence question, please someone help! Increasing, decreasing, or neither.
$$\left\{(1/3)^n \right\}$$
It said to compare the forms an and an+1
an = (1/3)^n
an+1 = (1/3)^n+1
It says a n = (1/3)^n is > then a n+1 = (1/3)^n+1 for all positive vales of n
and therefore it's decreasing.
How did they determine it's decreasing? I'm still confused. Did they plug in something to determine it?
+130511 Notice if we have
(1/3)n and n = 2, we have (1/3)2 = 1/9
But notice if we have n + 1 and n = 2.....we have (1/3)2+ 1 = (1/3)3 = 1/27
So....as long as n > 0 ......a n > an+1 because an+1 multiplies an by another (1/3).....thus making an+1 < an
Thus....this is a decreasing function as n gets larger......
Does that make sense??
