e is usually defined as :
Its equivalence to the form can be proved by many methods including using the generalized binomial theorem or directly the Taylor series.
http://en.wikipedia.org/wiki/Taylor_series
hello,
i don't know how to do proving the existence of e ....
okay, i know that it is by definition :
or
I have no idea how to do it, can some one help me with these please
P.S. I'm really really sorry if this shouldn't be posted here
e is usually defined as :
Its equivalence to the form can be proved by many methods including using the generalized binomial theorem or directly the Taylor series.
http://en.wikipedia.org/wiki/Taylor_series
thanks
hm... it should not (i think) be shown existence of e using Taylor series, because this we will not do Taylor series for long time ....
i do't have problem using "e" like it is defined... (lol solved a lot problems using that) but when it comes to prove it's existence i'm think i really don't get it... probably i'm having to much problem of figure it out theoretically, and understanding it to
If we accept the definition...
(1)
... what You have to demonstrated it that the limit exists. From the Newton's expansion...
(2)
... it is evident that...
a) the sequence is increasing with n and for is ...
b) (3)
Now is , so that...
(4)
... and from (4) You derive that for all n is . The conclusion is that the limit (1) exists and is . For the 'pratical' computation of e the (1) is very slow and is better the relation found by Isaac Netwon himself...
(5)
Kind regards