Question

Calculați:
a) S= 1+2+...+100;
b)S=2+4+6+...+500;
c)S=1+4+7+...+301;
d)S=5+10+15+...+2000;
e)S=51+52+...+100.
Va roog e urgent

Answer 1

a) 1 + 2 + 3 +.......+100 = 100·101/2 = 5050
b)  2(1+ 2 + .......+250) = 2·250·251/2 = 62750
c) 1 + (1+3·1) + (1+3·2) + (1+3·3)+.....+(1+3·100) = 1·101 +3(1+2+...+100) = =101 +3·100·101/2 = 101(1 + 150) = 101·151 = 15251
d) 5(1+2+3+....+400) = 5·400·401/2 = 401000
e)  S = 1+2+3+......100 - (1+2+ .....+50) = 100·101/2 - 50·51/2 = 50(202-51)/2
25·151 = 3775