Question
If $0<c<1$, show that $c^n \rightarrow 0$; and if $c>0$, show that $c^{1 / n} \rightarrow 1$. [Hint: Use Bernoulli's inequality for each, once with $c=1 /(1+x), x>0$ and once with $c^{1 / n}=1+x_n$, where $\left.x_n>0.\right]$
Step 1
Recall that Bernoulli's inequality states that for any real number \( x > -1 \) and integer \( r \geq 0 \), we have \( (1 + x)^r \geq 1 + rx \). Show more…
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