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# what is the sum of the squares of the first n positive

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Manager
Joined: 05 Sep 2007
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what is the sum of the squares of the first n positive [#permalink]  06 Mar 2008, 19:03
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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 S?
A. (3/4)S
B. (1/2)S
C. (4/3)S
D. (1/4)S
E. (1/8)S
VP
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Re: PS: Sum of squares [#permalink]  06 Mar 2008, 19:54
el1981 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 S?
A. (3/4)S
B. (1/2)S
C. (4/3)S
D. (1/4)S
E. (1/8)S

D

pick numbers

n =3

sum of the squares of the first3 positive integers = 14

squares of the first 3even positive integers =56

14/56 *S
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Re: PS: Sum of squares [#permalink]  06 Mar 2008, 20:15
el1981 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 S?
A. (3/4)S
B. (1/2)S
C. (4/3)S
D. (1/4)S
E. (1/8)S

sum of the squares of the first n +ve even integers
s = 2^2 + 4^2 + 6^2 + .......... + n^2

sum of the squares of the first n +ve integers
= 1^2 + 2^2 + 3^2 + .......... + (n/2)^2
= (2/2)^2 + (4/2)^2 + (6/2)^2 + .......... + (n/2)^2
= (1/2)^2 (2^2 + 4^2 + 6^2 + .......... + n^2)
= (1/4) (2^2 + 4^2 + 6^2 + .......... + n^2)
= (1/4) (s)
= s/4

which D.
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Re: PS: Sum of squares [#permalink]  07 Mar 2008, 03:48
Choosing numbers = use 2

first 2 positive even numbers is 2 ^2 + 4 ^ 2 = 4 + 16 = 20 = S

first 2 positive numbers is 1 + 4 = 5

looking at the answer 20/4 = 5 . Looks like D. Question is , should I test it using a bigger list of numbers to verify this answer or this is where i should end my quest. ?
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Re: PS: Sum of squares [#permalink]  08 Mar 2008, 08:17
Ok..then whats the OA and what is teh source of the question?
Re: PS: Sum of squares   [#permalink] 08 Mar 2008, 08:17
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