Convergence of a Monotonic Sequence

n

2

m

2

The plot shows the function

f(x)=1-

mx

1-

1

n

at the points

x=1,2,3,….

The pair of green lines meet at a point

(x,f(x))

—you can click or drag the lines to change it. Dragging to the right increases how much of the domain of the function is visible. The blue line is the limit of the function as

x∞

.