/sci/ - Science & Math

how many beetles died in this fire?

Can somebody please help with the following problem?

Let [math]x_m \in R^{\omega} [/math] where [math] x_m = (\frac{1}{m},\frac{1}{m+1},\frac{1}{m+2}, \cdots) [/math]. Show that [math] x_m [/math] converges to the zero sequence [math] 0 = (0,0,0,\cdots) [/math] in the product topology but not the box topolgy.