Question

se considra numerele a= 1+2+3+...+211

Answer 1

a = 1+2+...+211
= 211 * 212 : 2
= 211*106

b = 2+4+...+210
= 2(1+2+...+105)
= 2 * 105 * 106 : 2
= 105*106

c = 1+3+5+...+203
= 1 + 2+1 + 3+2 +...+ 102+101
= 1+2+3+...+102 + 1+2+...+101
= 102*103:2 + 101*102:2
= 51*103 + 101*51
= 51(103+101)
= 51*204
= 10404

a-b-c = 211*106 - 105*106 - 10404
= 106(211-105) - 10404
= 106*106 - 10404
= 11236 - 10404
= 832