Each of the sequences given below converges to zero. Specify the smallest value of (n_{varepsilon}) so that
Question:
Each of the sequences given below converges to zero. Specify the smallest value of \(n_{\varepsilon}\) so that \(\left|x_{n}ight|<\varepsilon\) for every \(n>n_{\varepsilon}\) as a function of \(\varepsilon\).
a. \(x_{n}=n^{-2}\)
b. \(x_{n}=n(n+1)^{-1}-1\)
c. \(x_{n}=[\log (n+1)]^{-1}\)
d. \(x_{n}=2\left(n^{2}+1ight)^{-1}\)
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: