I suspect this limit is 0, but how can I prove it?
limn→+∞2nn!
Answer
The easiest way to do this is to do the following: Assume n≥4. Then 0≤2nn!=n∏i=12i=2⋅2⋅21⋅2⋅3⋅n∏i=42i≤86⋅n∏i=124=86⋅2n−3. Applying the squeeze theorem gives the result.
I suspect this limit is 0, but how can I prove it?
limn→+∞2nn!
Answer
The easiest way to do this is to do the following: Assume n≥4. Then 0≤2nn!=n∏i=12i=2⋅2⋅21⋅2⋅3⋅n∏i=42i≤86⋅n∏i=124=86⋅2n−3. Applying the squeeze theorem gives the result.
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