Answer:
All of them
Step-by-step explanation:
According to the ratio test, for a series ∑aₙ:
If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.
If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.
(I) aₙ = 10 / n!
lim(n→∞) |(10 / (n+1)!) / (10 / n!)|
lim(n→∞) |(10 / (n+1)!) × (n! / 10)|
lim(n→∞) |n! / (n+1)!|
lim(n→∞) |1 / (n+1)|
0 < 1
This series converges.
(II) aₙ = n / 2ⁿ
lim(n→∞) |((n+1) / 2ⁿ⁺¹) / (n / 2ⁿ)|
lim(n→∞) |((n+1) / 2ⁿ⁺¹) × (2ⁿ / n)|
lim(n→∞) |(n+1) / (2n)|
1/2 < 1
This series converges.
(III) aₙ = 1 / (2n)!
lim(n→∞) |(1 / (2(n+1))!) / (1 / (2n)!)|
lim(n→∞) |(1 / (2n+2)!) × (2n)! / 1|
lim(n→∞) |(2n)! / (2n+2)!|
lim(n→∞) |1 / ((2n+2)(2n+1))|
0 < 1
This series converges.
Answer: so what you would do is would would take the first number that being -2 and add it to the problem like this y=2(-2)+1 and what you do is you times 2 and x2 which give you -4 then you add 1 which gives you -3 so y = -3
Step-by-step explanation:
Y=2(-2)+1 Y=2(-1)+1
-4+1 -3+1
-3 -2
y=2(0)+1 Y=2(1)+1
0+1 2+1
0 3
y=2(2)+1
4+1
5
Answer:
Not all labels will be used. ... They charge a certain rate for the rental of a sailboat and an additional ... according to the length of time for which the tourists rent the boat.
Answer:
the 4th graph.
Step-by-step explanation:
by solving for Y in the first equation, we get the y-intercept of -1 and the second equation has a y-intercept of 1. 4th graph is the only graph with those 2 intercepts
