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# Let R be a sum of 30 first members of a row: 1^2, 2^2, 3^2,

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SVP
Joined: 03 Feb 2003
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Let R be a sum of 30 first members of a row: 1^2, 2^2, 3^2, [#permalink]  30 May 2003, 02:00
Let R be a sum of 30 first members of a row: 1^2, 2^2, 3^2, and so on. Is R odd or even? Why?

Manager
Joined: 25 May 2003
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R is odd

why?

R=1^2 + 2^2....+30^2
=odd + even ....+even

between 1^2 and 30^2 there is an odd number of squares which are odd, therefore sum of squares is odd
SVP
Joined: 03 Feb 2003
Posts: 1607
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skoper wrote:
R is odd

why?

R=1^2 + 2^2....+30^2
=odd + even ....+even

between 1^2 and 30^2 there is an odd number of squares which are odd, therefore sum of squares is odd

Intern
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explaination [#permalink]  01 Jun 2003, 20:47
odd + odd = even ------ sum 14 odd numbers -- (1)

even + odd = odd ------ sum (1) with the remaining odd number,
which is only one --- (3)

even + even = even --------- sum 15 even numbers -- (2)

Thus, (3)+(2) = odd + even = odd

right and clear ?
explaination   [#permalink] 01 Jun 2003, 20:47
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