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 4p= 32
2 17g
3 176 + 5
4 3x or x/3 (not too sure)
5y+2 i think because those are parallel lines:)
Answer:
(3×3)+2=11
$11
Step-by-step explanation:
Remember to follow PEMDAS, and left -> right rule.
First, solve the Parenthesis:
(4 + 2^3)
Solve the exponent.
2^3 = 2 x 2 x 2 = 4 x 2 = 8
4 + 8 = 12
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(5^2) x (12)
5^2 = 5 x 5 = 25
25 x 12
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Multiply
25 x 12 = 300
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300 is your answer
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<em>~Rise Above the Ordinary</em>
