a) what distinguishes convergent sequences and divergent sequences.
Convergent sequences: Imagine an over-weight goddess who is anxious to lose weight. She swears, “Every day, I will eat half the food I eat the day before.” Also imagine she will live even without food but of course in bad mood without enough daily supply. The first few days, she lives okay and feel happy about the loss of the weight. But as time goes on, every day she eats almost nothing (and cries every day because of hunger).
Divergent sequence: For example, if an ambitious man (this man will live forever! ) learns 1 English word the first day and learns 2 words the second day… When he is really old, this old man have to learn countless words a day, which is really sad.
b)what distinguishes convergent series and divergent series.
Convergent series: Imagine a disaster happened on December 21st, 2012. On the earth, only a robot boy and his dog survived (and a piece of bread). The robot boy doesn’t need to eat, but the dog has to. Imagine this dog won’t die if he eats a little every day. And in order to save food, the boy gave 1/2 of he bread the first day and 1/2 of the remaining bread the second day… As time goes on, total amount of food the dog eats will be ONLY ONE PIECE OF BREAD.
Divergent series: For example, if one man (suppose he is a safe guard in Bank of Heaven and he is so cautious that nobody is able to catch him) steals a coin from a bank every day. When he is extremely old, he will have a lot of fortune that no one knows the exact number. What a lucky thief!
I cannot stop laughing… if every day our assignment is of so much fun, the sum of fun I have during my life ( suppose I am a goddess with infinite life) will be infinite fun!