Is Sequence xn Unbounded? Quickest Solution

[gottfried]

Homework Statement

Is the sequence x_n=[(n⁵+7n+3)⁷]/[(7-n⁴)⁶] bounded?


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The Attempt at a Solution

I've managed to tell that the sequence is not bound because as n tends to ∞ x_n also tends to ∞ but it took me a relatively long time.
Is there any way of telling this by just looking at the exponents or what is the quickiest way to tell that this sequence will get infinitely large.

 

[LCKurtz]

Homework Statement

Is the sequence x_n=[(n⁵+7n+3)⁷]/[(7-n⁴)⁶] bounded?


]

The Attempt at a Solution

I've managed to tell that the sequence is not bound because as n tends to ∞ x_n also tends to ∞ but it took me a relatively long time.
Is there any way of telling this by just looking at the exponents or what is the quickiest way to tell that this sequence will get infinitely large.

The highest degree of n in the numerator is 35 and in the denominator is 24. That's all you need to know.

 

[gottfried]

I was pretty sure it was something simple. Thanks!