SOLUTION: I need to learn how to tell the difference between converge and diverge

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Question 970720: I need to learn how to tell the difference between converge and diverge
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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%28600%2C600%2C-20%2C20%2C-100%2C100%2C10%2A1.5%5Ex%29

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%28600%2C600%2C-20%2C20%2C-100%2C100%2C1000%2A.5%5Ex%29

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

the solution is converging on 0.