Find the sum of the multiples of 5 or 3 under 553
For example, if we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
553 -1 =552
552/3 =184 terms
Sum of 184 "3's" =51,060.
553 - 3=550
550/5 =110 terms
Sum of 110 "5's" =30,525
+2498 \(553\div5=110.6\)
there is 110 numbers wich is devisible by 5
\(553\div3=184.333\)
there is 184 numbers wich is devisible by 3
\(553\div15=36.9\)
there is 36 numbers wich is devisible by both 5 and 3
now let s find sum of devisors of 5:
\(5+5\times2+5\times3+5\times4\dots+5\times110\\ 5(1+2+3+4\dots+110)\\ 5(55.5\times110)=30\ 525\)
sum of devisors of 3:
\(3(92.5\times184)=51\ 060\)
sum of devisors of both 5 and 3
\(15(18.5\times36)=9990\)
\(30\ 525+51\ 060-9990=71\ 595\)
