Help With Math Please

Question

Use Gauss's approach to find the following sums (do not use formulas) a. 1+2+3+4+....1001 b. 1+3+5+7+....+1001

Answer 1

a) 1 + 1001 = 1002; 2 + 1000 = 1002 ... 500 + 502 = 1002; 501

500(1002) + 501 = 501501

b) 1 + 1001 = 1002; 3 + 999 = 1002 ... 499 + 503 = 1002; 501

(500/2)(1002) + 501 = 251001