huh bad luck ????????? no wayyy im a super hero
Number Theory
Level
1
((1+2+3+4+5+........+100)^{2}) \times 2 \times 3 \times 4 \times 5 - (250 \times 5)
3365748345
3038528495
3237452907
3149650769
3060298750
3192438717
3365278346
3256439865
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
First, we can find that the sum of 1 to 100 is 5050:
(1 + 2 + 3 + ... + 98 + 99 + 100) + (100 + 99 + 98 + ... + 3 + 2 + 1) = 101 + 101 + 101 + ... + 101 = 10100, and dividing by 2 (since we counted each twice) is 5050.
Now (5050^2)(1 2 3 4 5) = [100(505)][(505)(120)] = 50500 * 60600 = (5)(6)(100^2)(101^2) = 300000(10201) = 3060300000
Finally, subtracting 250*5 = 1250 from 3060300000 gives 3060298750.