Question

Compute the limit. (Sequences/series).

Answer 1

from some reason the first thing that comes to mind when looking at that is the following:
\[\lim_{p \rightarrow \infty}(1+\frac{x}{p})^{p}=e^{x}\]

Answer 2

but anyways
if I were you I would try using y=e^(ln(y)) since the one there doesn't exactly match the above

Answer 3

thought if you prefer to use that earlier form I mentioned I suggest multiply the exponent in your question by 2/3*3/2

Answer 4

\[2n^2+3= \frac{3}{2} \cdot \frac{2}{3}(2n^2+3) =\frac{2}{3}(3n^2+\frac{9}{2}) \\ =\frac{2}{3}(3n^2+\frac{2}{2})+\frac{2}{3}(\frac{7}{2}) \\ =\frac{2}{3}(3n^2+1)+\frac{2}{3}(\frac{7}{2}) \]
use law of exponents