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The sum of several consecutive positive integers is equal to 1000 . Find all such numbers.

I don't know where to start , and how to start in solving this question. So please help.

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  • Start with basic algebra : if the smallest of $n$ consecutive integers is $a$. then the integers are $a,a+1,...a+n-1$. Now the sum of these is equal to $1000$. Use the formula for the sum of first $n-1$ natural numbers, to obtain $1000$ as a product of some terms in $a$ and $n$. Now use the various factors of $1000$ to fit pieces. – Sarvesh Ravichandran Iyer Aug 15 '18 at 04:47

1 Answers1

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Hint:

  • From arithmetic sum: $$\frac{n(2a+n-1)}{2}=1000$$

  • Think about factorization.

Siong Thye Goh
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