mathshead
what the name of the numbers 1+ (1/2) + (1/3) + (1/4)+...+...+.....(1/n)...
can something one tell me wheather it has a finit sum or not
can something one tell me wheather it has a finit sum or not
This is probably where your problem resides. The fact that the numbes get "smaller and smaller" is not enough to insure convergence, as you just witnessed. They need to get smaller "fast enough", so to speak.Originally posted by STAii
...then i was told "since the numbers are getting smaller and smaller, they add up to give a number (not infinity)".
Just to clarify, I thik this is a sufficient condition, not a necessary one (1/n and 1/n^2 both fail the criterion, yet the latter is convergent).Originally posted by HallsofIvy
One idea of "how fast" numbers in an infinite series must get smaller is the "ratio test":
The series [SIGMA] a_{n} converges if
lim |a_{n}|/|a_{n+1} is less than 1