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??
Follow Math Help Forum on Facebook and Google+
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 $\displaystyle x_n = \cos n$ and $\displaystyle y_n = \frac 1{\cos n}$ ?
or $\displaystyle x_n=y_n=(-1)^n=-1,1,-1,1,.....$ so $\displaystyle x_ny_n=1,1,1,1,.....$
Originally Posted by matheagle or $\displaystyle x_n=y_n=(-1)^n=-1,1,-1,1,.....$ so $\displaystyle x_ny_n=1,1,1,1,.....$ 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
Or, how about $\displaystyle x_n=0,1,0,1,0,1...$ and $\displaystyle y_n=1,0,1,0,1,0...$ so $\displaystyle x_ny_n=0,0,0,0,0,0...$.
View Tag Cloud