Thread: {a_n} converges => {a_n} is Cauchy; brief question

Prove. {a_n} converges, then it is Cauchy.

I think I already got the answer. Can someone let me know if I'm allowed to start like this.

|a_n - L|< e for n>N, and
|a_m - L|< e for m>N

|a_n - a_m| = |(a_n - L) - (a_m - L)|...

Originally Posted by cgiulz

Prove. {a_n} converges, then it is Cauchy.

I think I already got the answer. Can someone let me know if I'm allowed to start like this.

|a_n - L|< e for n>N, and
|a_m - L|< e for m>N

|a_n - a_m| = |(a_n - L) - (a_m - L)|...

... ... yes, it is indeed correct!