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.
For compounding interests, we use the equation F = P (1+i)^n where F is the future amount of the principal amount, P, in n years. Take note that the interest to be used should be the effective interest rate. In this case, it is already the effective interest rate.
F = P (1+i)^n
F = $4000 (1+.055)^4
F = $4955.2986
Answer:
3x-4
Step-by-step explanation:
y=ax+b general type of the line
a is the slope
y=3x+b
put 5 instead of the x and put 11 instead of the y
11=15+b
b=(-4)
Equation is 3x-4
Answer:
7 socks were sold
Step-by-step explanation:
7*8=56
11-7=4
4×11=44
56+44=100
This proves the answer of 7 to be correct
