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DIA [1.3K]
3 years ago
13

20 points!!!! Consider the series 3/10 + 3/2 + 15/2 + 75/2 + 325/2 + ... .

Mathematics
2 answers:
Mademuasel [1]3 years ago
6 0
It would converge at is you can make
mrs_skeptik [129]3 years ago
4 0

Answer:

Diverges

Step-by-step explanation:

Ratio of the consecutive terms is greater than 1, therefore series diverges

Ratio = (75/2) ÷ (15/2) = 5

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A binary operation is defined on the set of real numbers ℝ by
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Answer:

I. m = 2401

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Step-by-step explanation:

I. Determination of m

x ∆ y = x² − 2xy + y²

2 ∆ − 5 = √m

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II. Simplify ((n+1) ∆ y)/n

We'll begin by obtaining (n+1) ∆ y. This can be obtained as follow:

x ∆ y = x² − 2xy + y²

(n+1) ∆ y = (n+1)² – 2(n+1)y + y²

(n+1) ∆ y = n² + 2n + 1 – 2ny – 2y + y²

(n+1) ∆ y = n² + 2n – 2ny – 2y + y² + 1

(n+1) ∆ y = n² – 2ny + y² + 2n – 2y + 1

(n+1) ∆ y = n² – ny – ny + y² + 2n – 2y + 1

(n+1) ∆ y = n(n – y) – y(n – y) + 2(n – y) + 1

(n+1) ∆ y = (n – y + 2)(n – y) + 1

((n+1) ∆ y)/n = [(n – y + 2)(n – y) + 1] / n

((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

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