guest27

[help]

Uncle Arthur is completely mad. He adds up all of the even numbers
between 0 and 1000 (including the number 1000), then he adds up all
of the odd numbers between 0 and 1000, and finally he calculates the
difference between the two totals. What answer does he get?

[hermanmunster]

1) A headache

2) 500

The difference is 5 for every 5 even numbers added up compared with the associated odd numbers :

2+4+6+8+10 =30
1+3+5+7+9 = 25

1000=10*100 therefore the difference is 100*5 = 500. I definitely have a headache now

[naga]

Uncle Arthur is completely mad. He adds up all of the even numbers
between 0 and 1000 (including the number 1000), then he adds up all
of the odd numbers between 0 and 1000, and finally he calculates the
difference between the two totals. What answer does he get?

DEAR GUEST,

THE FORMULA FOR SUM OF EVEN NUMBERS IS N(N+2)/4 SO

WE HAVE TO PUT THE VALUE OF N AS 1000 ,THAT MEANS
1000(1000+2)/4=1000X1002/4=250500 AND
THE SUM OF ODD NUMBERS IS N*N/4

HERE AGAIN N IS 1000

1000*1000/4=1000*250=250000.

THE DIFFERENCE BETWEEN THE TWO TOTALS = 250500-250000=500.

[logan]

this can possibly done as follows;
the first set of even and the odd is 1&2 and the second set is 3&4 and so on. The last set is 999 & 1000. The difference on each is 1(one) and there are 500 such sets. So, is 500.

[ittiait]

The median of (even) numbers from 2 to 1000 inclusive is 501.
The median of (odd) numbers from 1 to 999 inclusive is 500.
Each sequence contains (1000 / 2 =) 500 numbers ...

... so the difference is [(501 - 500) x 500] 500.