Recent content by tim e

I posted the solution of that with r=1 in a similar thread called cauchy sequence problem

we have |x_(n+1)-x_n|<r ^n for all natural n and 0<r<1 we want te make |x_n-x_m|<ε by taking n and m sufficiently large. without loss of generality we can assume n<m. Then, defining k=m-n we have m=n+k so |x_n-x_m|=|x_n-x_(n+k)| Now, using the triangle inequality this yields...