Question

Can someone help explain why the limit of (10^n)/((-9)^(n-1)) is infinity as n goes towards positive infinity?

Answer 1

Hmm...well what I would do...is notice that

\[\large \frac{10^n}{9^{n -1}}\]

You can always write the denominator as a negative exponent to make this multiplication

so that would become

\[\large 10^n \times 9^{-(n-1)}\]
Distribute that '-' sign...
\[\large 10^n \times 9^{(1 - n)}\]

And the plug in the infinity....well a really big number times a really big number is still a really big number...so we arrive at infinity again