Question

The sum of all positive integers less than 400 which are not divisible by 5.

Answer 1

we will use the sum of natural number series formula
if S=1+2+3+4+........+n, then
S= n(n+1)/2
Now, sum of all +ve integers from 0 to 400 is given by
S=0+1+2+3+.......+400
=> S=400(400+1)/2;
=>S=80200;
Sum of all +ve integers divisible by 5 is given by
R=0+5+10+15+20+25+30+.........+400
R=5(1+2+3+4+5+6+.........+80)
R=5*80(80+1)/2
R=16200 ;
therefore the sum of all +ve integers <400 and not divisible by 5=S-R=64000