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# If x is equal to the sum of the even integers from M to N,

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If x is equal to the sum of the even integers from M to N, [#permalink]

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29 Jul 2006, 10:35
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If x is equal to the sum of the even integers from M to N, inclusive, and y is the number of even integers from M to N, inclusive, what is the value of x+y?
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29 Jul 2006, 16:34
Looks like both x and y are equal, unless the question was mistyped. This is a straightforward substitution problem, if you know the formula.

Sum of first N elements of Arithmetic progression: S = n/2 * (2a + (n-1)d)
where a = first term and d = common difference, n = no. of terms

For this problem:
a = M
d = 2 (even nos.)
n = (N-M)/2 +1 =

therefore
x = (N-M+1)/2 [2M + 2( (N-M)/2 + 1) ] = y

therefore x+y = 2x = (N-M+2)(N+M+2)/2
29 Jul 2006, 16:34
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# If x is equal to the sum of the even integers from M to N,

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