Thread: real-valued sequences

. Let

{xn} and {yn} be real-valued sequences.
Suppose xn ® +¥ and {yn} is bounded. Prove that yn / xn ® 0 .
how can i use the definitions of xn converges +¥ to and yn is bounded to prove this. and what value of epselon can i choose to show that the absuolt value of xn/yn is less that epselon. I will appraciate your help. Thanks.

Originally Posted by koko2009

. Let

{xn} and {yn} be real-valued sequences.

Suppose xn ® +¥ and {yn} is bounded. Prove that yn / xn ® 0 .
how can i use the definitions of xn converges +¥ to and yn is bounded to prove this. and what value of epselon can i choose to show that the absuolt value of xn/yn is less that epselon. I will appraciate your help. Thanks.

Hint: $\displaystyle \exists M\,\,s.t.\,\,\forall n\in \mathbb{N}\,,\,|y_n|\leq M\,,\,\,and\,\,\forall \epsilon >0\,\,\,\exists \,N_{\epsilon}\in \mathbb{N} \,\,s.t.\,\,n>N_{\epsilon}\Longrightarrow\,x_n>\fr ac{M}{\epsilon}$

Tonio