Question

Determine with limitrules if following sequence convergence, if yes then calculate its limit
\[a_{n}:=\frac{(-1)^{n}}{n} + \frac{n^{2}+14}{7+n-n^{2}}\] for \[n\geq1\]

Solution

\[\Large a_{n}:=\frac{(-1)^{n}}{n} + \frac{n^{2}+14}{7+n-n^{2}}= 0 + \frac{n^{2}(1+\frac{14}{n^{2}})}{n^{2}(\frac{7}{n^{2}}+\frac{1}{n}-1)} =\]

is it looks good or is it false ?

\[
\Large
\frac{1+0}{0+0-1}=\frac{1}{-1}=-1\]

Answer 1

yes good
too much work, but good

Answer 2

ok thank you :)

Answer 3

yw