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What is the sum of the squares of the first n positive integers if the
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12 May 2021, 09:42
12 May 2021, 09:42
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What is the sum of the squares of the first n positive integers if the sum of the squares of the first n even positive integers is A?
A. A(3/4)
B. A(1/2)
C. A(1/3)
D. A(1/4)
E. A(1/8)
A. A(3/4)
B. A(1/2)
C. A(1/3)
D. A(1/4)
E. A(1/8)
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Re: What is the sum of the squares of the first n positive integers if the
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12 May 2021, 09:48
12 May 2021, 09:48
1
Carcass wrote:
What is the sum of the squares of the first n positive integers if the sum of the squares of the first n even positive integers is A?
A. A(3/4)
B. A(1/2)
C. A(1/3)
D. A(1/4)
E. A(1/8)
A. A(3/4)
B. A(1/2)
C. A(1/3)
D. A(1/4)
E. A(1/8)
We want to determine the value of 1² + 2² + 3² + 4² + . . . + n²
Given: The sum of the squares of the first n EVEN positive integers is A
In other words: 2² + 4² + 6² + 8² + . . . + (2n)² = A
We can rewrite this as: (2 x 1)² + (2 x 2)² + (2 x 3)² + (2 x 4)² + . . . + (2 x n)² = A
Rewrite as: (2²)(1²) + (2²)(2²) + (2²)(3²) + (2²)(4²) + . . . + (2²)(n²) = A
Evaluate 2² to get: (4)(1²) + (4)(2²) + (4)(3²) + (4)(4²) + . . . + (4)(n²) = A
Factor to get: 4[1² + 2² + 3² + 4² + . . . + n²] = A
Divide both sides by 4 to get: 1² + 2² + 3² + 4² + . . . + n² = A/4
Answer: D
Cheers,
Brent
gmatclubot
Re: What is the sum of the squares of the first n positive integers if the [#permalink]
12 May 2021, 09:48
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