Please show how to prove that limn→∞n(12)n=0
Answer
Consider extending the sequence {n/2n} to the function f(x)=x/2x.
Then use L'Hopital's rule: limx→∞x/2x has indeterminate form ∞/∞. Taking the limit of the quotient of derivatives we get limx→∞1/(ln2⋅2x)=0. Thus limx→∞x/2x=0 and so n/2n→0 as n→∞.
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