Rate of convergence
Hey there kiddo, today I am going to tell you about something called "rate of convergence". It's a big, fancy term that tells us how quickly a sequence of numbers is approaching its limit.
Imagine you and your friend are racing towards a finish line. You both start at the same time and run towards the finish line. Now, let's say that your friend is faster than you. Because of this, she'll cross the finish line before you. However, over time you'll also get closer and closer to the finish line, until you eventually cross it as well. The speed at which you approach the finish line is called your "rate of convergence".
Similarly, if we have a sequence of numbers (for example, 1, 0.5, 0.25, 0.125, ...) that is approaching a limit (in this case, zero), the rate of convergence will tell us how quickly the numbers in the sequence get closer and closer to zero. If the numbers approach the limit quickly, we say the rate of convergence is "fast". If it takes a long time for the numbers to approach the limit, we say the rate of convergence is "slow".
There are different ways to measure rate of convergence, but one way is to look at how quickly the difference between the terms in the sequence and the limit approaches zero. In other words, we can ask ourselves how quickly the sequence "converges" towards its limit.
So there you have it, kiddo! Rate of convergence is a way of measuring how quickly a sequence of numbers approaches a limit. Just like you and your friend racing towards the finish line, the rate of convergence tells us how quickly the numbers in the sequence are getting closer and closer to their limit.
Imagine you and your friend are racing towards a finish line. You both start at the same time and run towards the finish line. Now, let's say that your friend is faster than you. Because of this, she'll cross the finish line before you. However, over time you'll also get closer and closer to the finish line, until you eventually cross it as well. The speed at which you approach the finish line is called your "rate of convergence".
Similarly, if we have a sequence of numbers (for example, 1, 0.5, 0.25, 0.125, ...) that is approaching a limit (in this case, zero), the rate of convergence will tell us how quickly the numbers in the sequence get closer and closer to zero. If the numbers approach the limit quickly, we say the rate of convergence is "fast". If it takes a long time for the numbers to approach the limit, we say the rate of convergence is "slow".
There are different ways to measure rate of convergence, but one way is to look at how quickly the difference between the terms in the sequence and the limit approaches zero. In other words, we can ask ourselves how quickly the sequence "converges" towards its limit.
So there you have it, kiddo! Rate of convergence is a way of measuring how quickly a sequence of numbers approaches a limit. Just like you and your friend racing towards the finish line, the rate of convergence tells us how quickly the numbers in the sequence are getting closer and closer to their limit.