Prove that if a sequence $s_n$ goes to a limit L as $n \rightarrow \infty $, then for a number $k > 0 $ then the sequence ${kn}$ will tend to the limi $kl$.
Is this simply because k is isolated from the limit, meaning that k has nothing to do with the converging part itself? moreover, how do I prove this?
Asked
Active
Viewed 43 times
0
user1090614
- 427
1 Answers
0
$|k\cdot s_n-k \cdot l|=k|s_n-l|\rightarrow 0 $
-
use \cdot instead of . to get expressions like $a \cdot b$ instead of $a.b$ – Tyler Nov 03 '13 at 04:42
-
can you please give a little explanation? how come it goes to zero? – user1090614 Nov 03 '13 at 13:39
-
1what does it mean to say $lim_{n\rightarrow \infty }s_n =l$ mean? – Nov 04 '13 at 07:08