How do I prove that: lim n → ∞ 4 n + 9 n 2 n = 4

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How do I prove that:       lim          n      →      ∞                          4        n            +      9              n        2              n    =  4

Raven Higgins · Accepted Answer

Squeeze theorem:For   n  ≥  4and so  4  ≤                    4        n            +      9              n        2              n    ≤      2          1              /            n        ×  4(We used   9      n    2    &amp;lt;      4    n   for   n  ≥  4, which has an easy proof using induction).Since       2          1              /            n        →  1 as   n  →  ∞, the result follows.To prove that       2          1              /            n        →  1 one way to see this is to use the following standard theorem:If       a    n    &amp;gt;  0 and       lim          n      →      ∞                  a              n        +        1                    a      n        =  L, then       lim          n      →      ∞            a    n          1              /            n        =  L. You pick       a    n    =  2. Of course, you could use this theorem on your original sequence itself...

How do I prove that: <munder> <mo form="prefix">lim <mrow class="MJX-TeXAtom-ORD">

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