Cauchy Criterion for Series limit

[sedaw]

need to prove there's limit by cauchy criterion

http://mathworld.wolfram.com/CauchyCriterion.html

the sequence: {X_n}=(10/1)(11/3)...(n+9/2n-1)

my try :

is that right ?

http://img155.imageshack.us/my.php?image=22221wl0.jpg

 

[mutton]

repost https://www.physicsforums.com/showthread.php?t=278987

 

[mathwonk]

for series, the cauchy criterion is essentially the fact that absolute convergence implies convergence.

 

[sedaw]

for series, the cauchy criterion is essentially the fact that absolute convergence implies convergence.

so... is it right ?

 

[mathwonk]

is what right?