limit of sequence as sum of series
If U is the limit of a sequence
u1,u2,u3,… |
of real or complex numbers, then U can be expressed as the series sum
U=u1+∞∑i=1(ui+1-ui). |
Proof. Let sn:=. We see that
for all Thus
Q.E.D.
Title | limit of sequence as sum of series |
---|---|
Canonical name | LimitOfSequenceAsSumOfSeries |
Date of creation | 2013-03-22 17:28:21 |
Last modified on | 2013-03-22 17:28:21 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 4 |
Author | pahio (2872) |
Entry type | Theorem |
Classification | msc 40-00 |
Related topic | SumOfSeries |