Last edited by Zii; 31-05-2012 at 01:03.
Convergence means when a series gets closer to a certain number.. And if n is a negative number, convergence occurs..
(Original post by Zii)
In general you may have
you must rewrite this by doing the following
it all hinges on it being "1 + something" inside the brackets.
then the modulus of the "something" (in our general case,
) must be less than one, so the original general case converges if
Edit: and remember, this is only for values of n which are anything but non-negative integers! If n is a non-negative integer, there is no issue of convergence.
But why is the expansion of
(1+x)-1 (where n is negative)
an infinite expansion? I mean n is negative so convergence should occur (so how can it be infinite)?
Last edited by xXxiKillxXx; 31-05-2012 at 01:23.
Last edited by EEngWillow; 31-05-2012 at 19:13.
Thanks a LOT!
Regarding the above, just to clarify if |x|<1, this means a series is convergent right? Also convergent means a series tends towards a certain value right?
(Original post by EEngWillow)
An infinite series can either converge or diverge. You can hopefully see the need for |x| < 1: you need a value between 0 and 1 for the terms to get smaller in value each time (take the example x = 0.5, so x^2 = 0.25, x^3 = 0.125 etc) -> under these circumstances the series converges. If you had instead x = 2, then each term would get larger (x = 2, x^2 = 4, x^3 = 8) and it diverges.
Last edited by xXxiKillxXx; 14-06-2012 at 15:59.