Let $\phi (n)$ be the Euler's totient function . Thenhow to prove that the set $\{\dfrac{\phi(n+1)}{\phi(n)}: n \in \mathbb Z^+\}$ is unbounded above that is how to show $\lim \sup_{n \to \infty} \dfrac{\phi(n+1)}{\phi(n)}= \infty$ ? Moreover , how to show that $\lim \inf_{n \to \infty} \dfrac{\phi(n+1)}{\phi(n)}= 0$ ?
2026-03-27 10:47:57.1774608477
how to show $\lim \sup_{n \to \infty} \frac{\phi(n+1)}{\phi(n)}= \infty$ and $\lim \inf_{n \to \infty} \frac{\phi(n+1)}{\phi(n)}= 0$?
222 Views Asked by user217921 https://math.techqa.club/user/user217921/detail AtRelated Questions in SEQUENCES-AND-SERIES
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