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:
growth
Step-by-step explanation:
5 is a positive number greater than 0 (not a decimal) making this growth
Formula for finding mean:
Mean = (a1 + a2 + ... + an) / n
Mean is another word for average; average number of a data set.
Problems with steps:
---------------------------------------------------------------------------------------
1) 9, 3, 6
Average = Sum/Count
Sum = 18/6
Count = 3
2) 14, 12, 17, 9
52/4
Mean = 13
3) 15,8,10,5,7
= 45/5
Mean = 9
4) 18,19,11
= 48/3
Mean = 16
5) 4,20,16,4
= 44/4
Mean = 11
6) 12,11,12,20,15
= 70/5
Mean= 14
7) 19,8,3
= 30/3
Mean = 10
8) 7,13,6,2
= 28/4
Mean = 7
9) 12,15,17,2,14
60/5
Mean = 12
10) 10,18,8
= 36/3
Mean = 12
11) 5,2 ,0,1
= 8/4
= 2
12) 3,9,5,16,7
= 40/5
Mean = 8
SOLVED !
Hope this helps!
- ROR
Answer:
60 feet
Step-by-step explanation:
a - 2x
b - x
c - 3x
120/6 = 20
20 x 3 = 60
Answer:
74 degrees
Step-by-step explanation:
As sum of interior and exterior at a vertex add to 180, subtract 106 from 180 to get 74 degrees
