Answer:
One convergence criteria that is useful here is that, if aₙ is the n-th term of this sequence, then we must have:
Iaₙ₊₁I < IaₙI
This means that the absolute value of the terms must decrease as n increases.
Then we must have:

We can write this as:

If we assume that n is a really big number, then:
n + 1 ≈ 1
And we can write:

Then we have the inequality

And remember that this must be in absolute value, then we will have that:
-1 < (x - 2)/3 < 1
-3 < x - 2 < 3
-3 + 2 < x < 3 + 2
-1 < x < 5
The first option looks like this, but it uses the symbols ≤≥, so it is not the same as this, then the correct option will be the second.
Answer:
x = -10; x = 7
Step-by-step explanation:
|2x + 3| - 6 =11
Add 6 to each side.
|2x + 3| = 17
Apply the absolute rule: If |x| = a, then x = a or x = -a.
(1) 2x + 3 = 17 (2) 2x + 3 = -17
Subtract 3 from each side
2x = 14 2x = -20
Divide each side by 2
x = 7 x = -10
<em>Check:
</em>
(1) |2(7) + 3| - 6 = 11 (2) |2(-10) + 3| - 6 = 11
|14 + 3| - 6 = 11 |-20 + 3| - 6 = 11
|17| - 6 = 11 |-17| - 6 = 1
1
17 - 6 = 11 17 - 6 = 11
11 = 11 11 = 11
Quadrant is III so, sign would be negative for Sec.
Now, we know, csc = H / P
So, H = 4, P = 3
Calculate for B,
B² = H² - P²
B² = 4² - 3²
B² = 16 - 9
B = √7
We know, sec Ф = H / B = 4 / √7
We can write it as: -4√7 / 7 [ -ve sign for 3rd quadrant ]
In short, Your Answer would be Option B
Hope this helps!