What is the difference between convergence and divergence? i'm in advanced algebra so try not to make a complicated answer. you.

The concept of convergence is a topic more suited to a discussion of calculus if you want a fairly rigorous explanation.

But what it basically means is that, given a function that depends on one or more independent variables, the value of the function will "converge" or approach a finite value as the independent variable(s) approaches their own finite values.

Divergence means the opposite. If there is no finite or fixed value that a function appears to be approaching, then it does not converge, and is thus said to diverge.

Some examples: As gets arbitrarily large, the function



will approach 0. You can see why this must be the case by checking what happens to the value of when is picked to be 10, or 1000, or 1000000000, and so on. Clearly, must be positive, but the large the denominator, the smaller the value of . It will never actually take on the value of 0, but we can see that it must *converge to* 0.

On the other hand, the function



will oscillate indefinitely between the values of -1 and 1, so this function is said to not converge to any specific value as increases indefinitely, which means diverges.