# sum of multiples

• Sep 11th 2007, 01:58 AM
Bartimaeus
sum of multiples
I just can't see it at the moment.

Find the sum of all positive integers less than 10,000 not divisible by seven.

Thanks guys.
• Sep 11th 2007, 02:12 AM
red_dog
From the sum of all positive integers less than 10000, substract the sum of all positive integers which are divisible by 7.
$\displaystyle\sum_{k=1}^{10000}k-\sum_{k=1}^{1428}7k$
and use $\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}{2}$