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Activity 8.1.4 .
Use graphical and/or algebraic methods to determine whether each of the following sequences converges or diverges.
(a)
\(\left\{\frac{1+2n}{3n-2}\right\}\)
(b)
\(\left\{\frac{5+3^n}{10+2^n}\right\}\)
(c)
\(\left\{\frac{10^n}{n!}\right\}\) (where
\(!\) is the
factorial symbol and
\(n! = n(n-1)(n-2) \cdots (2)(1)\) for any positive integer
\(n\) (as convention we define
\(0!\) to be 1)).
