been workin on this problem:

let An Bn and Cn be sequences satisfying

An<=Bn<=Cn for all n an element of the natural numbers

suppose that An->x and Cn->x, where x is a real number show that Bn->x

this is how i did it

[tex]A_n\le B_n\le C_n \forall n\epsilon N[/tex]

[tex]A_n\longrightarrow x,C_n\longrightarrow x\ \forall x\epsilon \Re[/tex]

[tex]\lim_{n\to\infty}A_n\le\lim_{n\to\infty}B_n\le\lim_{n\to\infty}C_n[/tex]

[tex]x\le\lim_{n\to\infty}B_n\le x[/tex]

therefore by the squeeze theorem [tex]B_n\longrightarrow x[/tex]

would this be correct, and are there any other ways of proving it?

thanxs