Examples of Limits of Real Sequences

n

1

ϵ

1

type

constant

increasing

decreasing

damped

periodic

Each of the sequences except for the periodic one appear to converge to 3. The

ϵ

slider lets you vary the tolerance limit in the definition of the limit. The

n

slider lets you plot the

th

n

element of the sequence. The color of the point representing the element of the sequence is green within the

ϵ

tolerance region, and red otherwise.