Question 970720
converge means to come together.
diverge means to spread apart.


when a solution converges, it means it is approaching a specific value.


it is converging to that value.


when a solution diverges, it means it is getting further and further away from a specific value.


if you look at a geometric progression, the solution will diverge if r is greaster than 1 and the solution will converge if the r is less then 1 and greater than 0.


here's a geometric progression when r is greater than 1.


the formula is y = 10 * 1.5^x.


{{{graph(600,600,-20,20,-100,100,10*1.5^x)}}}


as x increases, y increases as well, so the solution is diverging because it is not going towards any specific value.


here's the same equation where r is less than 1.


the formula is y = 10000 * .5^x


{{{graph(600,600,-20,20,-100,100,1000*.5^x)}}}


you can see that, as x gets larger, the value of y gets closer and closer to 0.


the solution is converging on 0.