Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Answer:
6
Step-by-step explanation:
Its 6 or 4, but leaning toward 6
11x° is interior angle of ladder to the ground
and 7X° is interior angle of ladder to the wall
exterior angle of a ladder to wall is 180-7x
and exterior angle of a ladder to ground is 180-11x
Answer: x = a*y + 3
Step-by-step explanation:
To make x the subject of the equation, first, we open the bracket
4x - 12/a = y
Then cross multiply:
4x - 12 = a * y ( a*y means the product of the two variables)
Add 12 to both sides of the equation
4x = a*y + 12
Divide both sides by 4 to get the value of x
x = a * y + 12/4
x = a*y + 3
I hope this helps.
