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:
1,1/9,2/3
Step-by-step explanation:
You keep the bottom number and just add or subract the top number
2/5+3/5= 1
8/9-7/9=1/9
3/3-1/3=2/3
Answer:
Yes, you can use this inequality to find the numbers of cars required.
Step-by-step explanation:
12 + 3n > 28 where n = the number of cars required
3n > 28 -12
3n > 16
n > 5 1/3
Greater than 5 1/3 gives 6 cars.
Which set of ordered pairs represents a function? A {(22, 5), (23, 10), (22, 7), (23, 5)} B {(22, 5), (26, 10), (23, 7), (23, 5)
balu736 [363]
Answer:
C
Step-by-step explanation:
A function is a special kind of relation in which each valid input gives exactly one output.
C {(22, 10), (23, 10), (24, 7), (25, 5)}
So C is the correct option.
Answer:
201.06
Step-by-step explanation:
A=πr2=π·82≈201.06193
