Can you use the inequality to prove the following?
It's been bugging me for quite long, I wanted to determine if a series is convergent or divergent.
By d'Alembert's criterion:
Then , so is divergent.
By Cauchy's criterion:
That's where I was left puzzled. Were the limit equal to zero, then by Cauchy's criterion the series would be convergent. Now that I know it's also , I have no more doubts.
Thanks a lot for your replies.
"e" is "Napier's constant," the number 2.718281828459045235360287471352662497757... This number has a lot of special properties, which I'll let you look up.
is a Math hieroglyph for the words "for all." It is most commonly used in set theory.
"ln()" is a logarithmic function, for example: , where e is Napier's number above.
-Dan