Answer: Hello there!
In your graph you can see two things, first, your function only has negative values (and decreasing, so it never is positive), and second, it intersects the x-axis in x = 3.
The first thing says to us that we should discard the second and third options, because they allow positive values for y (you can evaluate them in x = 10 for example, and see that y is positive).
Now we get the first and fourth options to analyze:
1)
2)
if you evaluate this functions in x = 3, y should be 0.
in the first equation this is trivial, and in the second you got:
y = 3/2 - 3 = -3/2
so this equation didn't give us 0.
Then the correct answer is the first option.
You can factor the 32 out of the sum:
We can also change the index as follows
Now, we have a theorem that states that the series
converges if and only if , and in this case we have
This is your case, because you have
which implies that your series converges, and the value is