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MATHEMATICS Convergent sequence
Welcome |
Theory
-
natural numbers ,
-
real numbers ,
-
sequence.
defined on the positive integers '
' . We are writing
,
for
n = 1, 2, 3, ...Definition ( limit of sequence ): We say, that the number g is the limit of the
if for any
there exists a natural number
such, that for each number
n
more (or equal) from the
(
)
there is
.
We are writing
.Theorem.
If a sequence
has limit a, and a sequence
has limit b ( where
), then
a)
,
( for all
) b)
,
c) 
,
d)
,
for
