find sum of pos ints <= 10,000 div by 3 or 11 but not both

[claudeluvstwilight]

Find the sum of all positive integers not greater than 10000 that are divisible by either 3 or 11 but not by both of them

Could someone please help me with this problem!!! Thanks SO much!

 

[tkhunny]

18,178,182

Computer programs are wonderfuil things.

 

[soroban]

Hello, claudeluvstwilight1

We are expected to be familiar with arithmetic series and this formula:

. . $\displaystyle \text{The sum of the first }n\text{ positive integers is: }\:\frac{n(n+1)}{2}$

Find the sum of all positive integers not greater than 10000
that are divisible by either 3 or 11, but not by both of them.

The sum of multiples of 3:

. . \(\displaystyle S_3\;=\;3 + 6 + 9 + \hdots + 9999 \;=\;3(1+2+3+\hdots+3333)\)
. . . . .$\displaystyle =\;3\cdot\frac{3333\cdot3334}{2} \;=\;16,668,333$


The sum of multiples of 11:

. . \(\displaystyle S_{11} \;=\;11 + 22 + 33 +\hdots+9999 \;=\;11(1+2+3+\hdots+909)\)
. . . . . $\displaystyle = \;11\cdot\frac{909\cdot910}{2} \;=\;4,549,545$


The sum of multiples of 33:

. . \(\displaystyle S_{33} \;=\;33+66+99+\hdots+9999 \;=\;33(1+2+3+\hdots+303)\)
. . . . . $\displaystyle = \;33\cdot\frac{303\cdot304}{2} \;=\;1,519,848$


$\displaystyle \text{Answer: }\;S_3 + S_{11} - 2\cdot S_{33} \;=\;16,668,333 + 4,549,545 - 2(1,519,848)$

. . . . . . . . $\displaystyle =\;\boxed{ 18,178,182}$

 

[Deleted member 4993]

Duplicate post:

http://answers.yahoo.com/question/index ... 412AA9PE49