Question

$\underset{n\to \infty }{lim}(3^n+5^n+7^n{)}^{\frac{1}{n}}$ equals to:

• A. $3$
• B. $5$
• C. $7$
• D. Does not exist

Answer 1

Answer: (C)

$7$

$\underset{n\to \infty }{lim}(3^n+5^n+7^n{)}^{\frac{1}{n}}$
$=\underset{n\to \infty }{lim}{\left[7^n({\left(\frac{3}{7}\right)}^n+{\left(\frac{5}{7}\right)}^n+1)\right]}^{\frac{1}{n}}$
$=7\cdot 1=7,[\because \underset{n\to \infty }{lim}{a}^n=0,$ if $|a|<1]$