Topology: product, uniform, and box topology converging sequences

I'm having a lot of trouble understanding how to work a problem like this from topology...

Consider the product, uniform, and box topologies on R^{w} (that's an omega)

In which topologies do the following sequences converge?

w_{1} = (1,1,1,1,...)

w_{2} = (0,2,2,2,...)

w_{3} = (0,0,3,3,...)

...

x_{1} = (1,1,1,1,...)

x_{2} = (0,1/2,1/2,1/2,...)

x_{3} = (0,0,1/3,1/3,...)

...

y_{1} = (1,0,0,0,...)

y_{2} = (1/2,1/2,0,0,...)

y_{3} = (1/3,1/3,1/3,0...)

...

z_{1} = (1,1,0,0,...)

z_{2} = (1/2,1/2,0,0,...)

z_{3} = (1/3,1/3,0,0...)

...

Any help would be great...even just one set of the variables so I could have an example of where to go...Thanks!

Re: Topology: product, uniform, and box topology converging sequences