Convergence

Consider this example sequence Or, as a function Plotting the graph, we notice some odd behaviour:

As we keep getting a larger and larger input this function's value keeps getting smaller and smaller. This function is monotone. Strictly decreasing, actually.

But, as it keeps getting larger and larger, it gets so close to 0, but never actually reaches it.

That's the reason the concept of Convergence exists.
For something to converge, it means to gradually get closer to something.

As we take an infinitely larger x in this case, we get closer and closer to zero. We say that our function/sequence converges to 0.

Next, we'll see what happens when we have Divergence