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2 votes

Computing the Limit $\lim_{n \to \infty} n\left[ \frac{a_{n+1}}{a_{n}} - \left(\frac{n}{n+1}\right)^{\frac{1}{3}} \right]$

The expression can be represented as $${n\over 2(n+1)}-\left ({n\over n+1}\right )^{4/3}\,[-(n+1)]\left [\left (1-{1\over n+1}\right )^{2/3}-1\right ]$$ The limit of the last two factors is equal by ...
Ryszard Szwarc's user avatar
1 vote
Accepted

Help understanding Spivak's solution, and a verification of my proof. Spivak Chapter 5, Question 3(vi)

OP's analysis is fine, but he makes a small mistake. On the one hand we have $1-\epsilon < \sqrt x < 1 + \epsilon$, which after squaring leads to $(1-\epsilon)^{2} < x < (1+\epsilon)^{2}$. ...
M. Wind's user avatar
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