The minimum distance between the asteroid and the sun is 10 - 6 =4
The given hyperbolic path defined as
divide both the sides by 576,
The general equation of
hyperbola is written as
;
Compare with above mention equation
Here
The distance between the asteroid and the sun is seen by figure -1
or
⇒c =10
The minimum distance between the asteroid and the sun is 10 -6 =4
There would be about a 14.3% chance of being able to see it
30 minutes / 210
.1428 =
14.3%
Assuming the series is

The series will converge if

We have

So the series will certainly converge if

, but we also need to check the endpoints of the interval.
If

, then the series is a scaled harmonic series, which we know diverges.
On the other hand, if

, by the alternating series test we can show that the series converges, since

and is strictly decreasing.
So, the interval of convergence for the series is

.
Answer:
I think that's right. I checked my answer and proved it on that sheet.