a) 1 +2 +3 +4 +......+98
98 +97 +96 +95+......+1
sum 99 +99 +99 +99+......+99
there are 98 of these sums, the total is 98 * 99 = 9702, since this sum is twice the sum of the numbers 1 thru 98, we have
sum 1 +2 +3 +4 +.....98 = 9702/2 = 4851
b) 1 +3 +5 +7+.....+1003
1003 +1001 + 999 +997 +....+1
sum 1004 +1004 +1004 +1004 +..1004
There are 502 of these sums. the total is 502 * 1004 = 504008, since this sum is twice the sum of the numbers 1 +3 +5 +7 +....1003, we have
sum 1 +3 +5 +7+.....+1003 = 504008/2 = 252004
