- #1
steven187
- 176
- 0
hello all
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
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