Interactive resource
Limits of sequences
Calculus. aₙ → L: for every ε > 0 there is N so that n > N ⇒ |aₙ − L| < ε. Free interactive GeoGebra resource — adjust parameters in the browser.
Overview
aₙ → L: for every ε > 0 there is N so that n > N ⇒ |aₙ − L| < ε.
Explanation
ε–N definition: for every ε > 0 there exists N such that n > N implies |aₙ − L| < ε.
Picture: eventually every term lies in the 2ε-wide tube about L.
Smaller ε usually forces a larger N.
How to use
Adjust ε and see when terms all enter the (L − ε, L + ε) tube.