A sequence is a function whose domain is the natural numbers. We use [math]a_k[/math] for the output of the sequence instead of a(k). [br][br]The graph of the sequence consists of isolated dots with natural number first coordinates. [br][br]We say that the infinite sequence converges to a limit L if and only if[br]for every positive number epsilon ([math]\epsilon>0[/math]) there exists a positive number M such that if k > M then [br][math]\left|a_k-L\right|<\epsilon[/math].[br][br]This formal definition is illustrated in the app above. [br] Enter a formula for the sequence in the input box using k as the independent variable.[br] Enter the value of its limit in the input box for L. Choose a value for epsilon. Manipulate M by moving point M on the x-axis.[br]If the choice of limit is correct, then you should be able to choose a value for M so that to the right of M the sequence always stays inside the shaded region, regardless of how small a value is chosen for epsilon.