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How can I work this one out (with workings)?

"Find the sum of all the integers between 1 and 1000 which are divisible by 7"

Thanks!

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You can just add up all the multiples of 7 which are less than 1000. The largest number of such numbers is

$7 \lfloor \dfrac{1000}{7} \rfloor=994$

Then, if you add all the multiples of 7 from 7 to 994,

$7+14+...+994=7(1+2+...\dfrac{994}{7})=7(1+2+...142)=7 \dfrac{(142)(143)}{2}=71071$

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Hint: $7\cdot(1+2+\ldots+\lfloor \frac{1000}{7}\rfloor)=?$.

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Hint: What is the largest multiple of $7$ less than $1000?$ Do you know how to sum $1+2+3+\dots$ up to $n?$ Distribute out the $7$

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