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Given that 1+2+3+......+9+10=55Find 1+2+3+......+999+1000=?What is the formula for finding it?
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joy067

by joy067 at June 06, 2011

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1+1000 + 2 + 999 + .... + 500 + 501 = 1001 + 1001 + ... 1001 = 500 * (1001) = 500500for any 1 + 2 + ... + n-1 + n1 + n + 2 + n-1 +... + (n/2) + (n/2)+1 = (n+1)(n/2)
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John_Doe John_Doe June 06, 2011

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The formula is (n/2)(a1 + an), "a1" being the first term, "an" being the last term, and n being the number of terms. So basically you are adding the first and last numbers and multiplying it by the number of pairs of terms you have.So, plugging the numbers in...(1000/2)(1 + 1000) = 500,500.
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JoshuaThomas JoshuaThomas June 06, 2011

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