# limit > M, then An> M?

• Sep 17th 2009, 12:17 PM
cgiulz
limit > M, then An> M?
Prove:

lim $a_{n}$ > M --> $a_{n}$ > M for n>>1 (large n).
• Sep 17th 2009, 02:27 PM
xalk
Quote:

Originally Posted by cgiulz
Prove:

lim $a_{n}$ > M => $a_{n}$ > M for n>>1.

Does n>>1 ,mean very large n ,or n equal or greater than 1??
• Sep 17th 2009, 04:56 PM
cgiulz
for large n.
• Sep 17th 2009, 07:33 PM
xalk
Then we have:

Since $\lim_{n\rightarrow\infty} a_{n} =l$>M THAT implies that for all ε>0 and hence for ε= l-M>0 ,there exists an N such that :

for all n , $n\geq N$ then $|a_{n}-l|< l-M$

or $M-l< a_{n}-l< l-M$.

Thus $a_{n}> M$ for large n biger or equal to N