2010005304
Level:
C
Find the limit of the following sequence.
\[
{\left({\left( \root{n}\of{0.5}+\frac{\root{n}\of{0.5}}
{n} \right)}^{n}\right)}_{
n=1}^{\infty }
\]
Hint: The limit of the sequence \({\left({\left(1 + \frac{1}
{n}\right)}^{n}\right)}_{n=1}^{\infty }\)
is the Euler number \(\mathrm{e}\).
\(\frac12 \mathrm{e}\)
\(\mathrm{e}^{\frac12}\)
\(\frac12 + \mathrm{e} \)
\(\infty \)