Question

Calculati sumele :
a) 42 + 43 + 44 + .. 347
b) 121 + 122 + 123 + ... + 854
c) 84 + 86 + 88 + ... + 684
d) 63 + 66 + 69 + ... + 537

Answer 1

1+2+3+.......+347=347x(347+1):2=347x348:2=120756:2=60378
1+2+3+.........+41=41x(41+1):2=41x42:2=1722:2=861
42+43+44+......+347=60378-861=59517

1+2+3+........854=854*855/2=365085
1+2+3+......120=120*121/2=7260
121+122+123+...+854=365085-7260=357825

2+4+6+.......684=2(1+2+3+....+342)=2*342*343/2=117306
2+4+6+.......82=2(1+2+3+....+41)=2*41*42/2=1722
84+86+88+...+684 =117306-1722=115584

3+6+9+.......537=3(1+2+....+179)=3*179*180/2=48330
3+6+9+.......60=3(1+2+....+20)=3*20*21/2=630
63+66+69+....537=48330-630=47700