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.
F(x) = input the x
3x+2
multiply it by 3 and add 2
3*x+2=
3*5+2=
15+2 =
17
or if you meant 2x:
it would be the same just do:
3+2x
3+2*5
3+10
13
Answer:
B) 4,608.
Step-by-step explanation:
A square pyramid with the maximum volume that can fit inside a cube has a same base as a cube ( 24 cm x 24 cm ) . The height of the pyramid is also same as a side length of a cube ( h = 24 cm ).
The volume of the pyramid:
V = 1/3 · 24² · 24 = 1/3 · 576 · 24 = 4,608 cm³
Answer:
The maximum volume of the pyramid is 4,608 cm³.
It would go in quarderent 4
Answer:
13 and 23
Step-by-step explanation:
create an equation to solve:
(2x-3) + x = 36
3x - 3 = 36 combine like terms
<u> +3 +3</u><u> </u> add 3 to both sides
<u>3</u>x = <u>39</u>
3 3 divide both sides by 3
x = 13
<u>13 is the first number</u>
the 2nd number is 3 let than twice the first so we create and solve a new equation:
2x - 3 = ?
2(13) = ? substitute 13 from the
smaller number to solve
<u>23 = the 2nd number</u>
