I genuinely don't know what the point is of the table, where do you use it for?
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:
(25)-(3)
Step-by-step explanation:
Answer:
Step-by-step explanation:
This question is asking you to insert two equations, f(x) and g(x), into the equation g(x) - f(x). This will lead to the equation below.
Now we can solve for the equation.
Answer:
There is no solution
Step-by-step explanation:
4x - 2y = 5 --> 4x - 2(2x + 10) = 5
4x - 4x - 20 = 5
4x - 4x -25 = 0
Final answer is -25 = 0 and so therefor it is no solution
