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If the sum of the first 500 positive integers is k, what is the sum of
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08 Feb 2022, 05:00
08 Feb 2022, 05:00
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45% (01:47) correct
54% (01:44) wrong based on 11 sessions
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If the sum of the first 500 positive integers is k, what is the sum of the first 1000 positive integers in terms of k?
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2k+250,000
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Re: If the sum of the first 500 positive integers is k, what is the sum of
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24 Feb 2022, 23:48
24 Feb 2022, 23:48
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Carcass wrote:
If the sum of the first 500 positive integers is k, what is the sum of the first 1000 positive integers in terms of k?
Show: ::
2k+250,000
Average of first n cons. integers = \(\frac{(Last + First)}{2}\)
Sum = (Average)(number of terms)
\(k\) = Sum of first 500 +ve integers = \(\frac{(500 + 1)}{2}(500) = (501)(250)\)
Sum of first 1,000 +ve integers = \(\frac{(1,000 + 1)}{2}(1,000) = (1,001)(500)\)
Rewrite \((1,001)(500)\) as \((501 + 500)(250 + 250)\)
\((501)(250) + (501)(250) + (500)(250) + (500)(250)\)
\(k + k + 2(500)(250)\)
\(2k + (500)(500)\)
\(2k + 250,000\)
General Discussion
Re: If the sum of the first 500 positive integers is k, what is the sum of
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14 Sep 2023, 08:06
14 Sep 2023, 08:06
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