1. ## true or false

if neither sequence {Xn} and {Yn} converges then {XnYn} does not converge

i think this is false but am failing to find a counter-example?
and ideas??

2. Originally Posted by crafty
if neither sequence {Xn} and {Yn} converges then {XnYn} does not converge

i think this is false but am failing to find a counter-example?
and ideas??
how about $x_n = \cos n$ and $y_n = \frac 1{\cos n}$ ?

3. or $x_n=y_n=(-1)^n=-1,1,-1,1,.....$
so $x_ny_n=1,1,1,1,.....$

4. Originally Posted by matheagle
or $x_n=y_n=(-1)^n=-1,1,-1,1,.....$
so $x_ny_n=1,1,1,1,.....$
this was the example i had way in the back of my mind. i was grasping for it, but came up with what i posted earlier.

both work though

$x_n=0,1,0,1,0,1...$
$y_n=1,0,1,0,1,0...$
so $x_ny_n=0,0,0,0,0,0...$.