I can't seem to figure out how to find this seemingly simple limit (that is shown numerically to go to 0)(adsbygoogle = window.adsbygoogle || []).push({});

lim_{x → ∞}( x r^{x})

for r < 1

This is an indeterminate form of∞ * 0, but when I try to apply L'Hôpital's rule as

lim_{x → ∞}( r^{x}/ ( 1 / x ) )

I end up getting an expression of the formx, with further application of the rule generating higher and higher powers of^{2}r^{x}x

I'm totally stuck!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help me find this limit!

**Physics Forums | Science Articles, Homework Help, Discussion**