# Math Help - Limit of (-1)^n(1/n^3)cos(n^3)

1. ## Limit of (-1)^n(1/n^3)cos(n^3)

See http://www.wolframalpha.com/input/?i...+n-%3Einfinity.

This is a sequence, not a series.

I need to prove that this converges to 0.

I have thought about trying a proof by contradiction, and the comparison test (cos(n^3)/n^3) is always smaller than 1/n^3.

I have thought about breaking up the limit into individual parts, but I still get 0 times a divergent.

Thank you.

2. Originally Posted by runningeagle
See - Wolfram|Alpha.

This is a sequence, not a series.

I need to prove that this converges to 0.

I have thought about trying a proof by contradiction, and the comparison test (cos(n^3)/n^3) is always smaller than 1/n^3.

I have thought about breaking up the limit into individual parts, but I still get 0 times a divergent.

Thank you.
Note:
1. The numerator is bounded for all values of n.
2. Denominator --> +oo as n --> +oo.