Răspuns:
5. a) (-1+3)+(-5 +7)+( -9 +11) +(-13 +15)+(-17+19)+(-21+23)+(-25 +27)+(-29+31)=
= 2*8=16
b) (-2+4)+(-6+8) +....+(-38+40)= 2+2+ ...+2 =2*10=20 ( sunt 20 termeni daca ii grupam cate 2 vom avea 10 grupe de 2)
c) (-1008-1007 -...-2-1) + (1+2+3+4+...+1008+1009)=
(1+2+3+4+...+1008+1009)= 1009*1010:2= 1009*505
(-1008-1007 -...-2-1)= - ( 1+2+...+ 1007+1008)= - 1008*1009:2= -504*1009
(-1008-1007 -...-2-1) + (1+2+3+4+...+1008+1009)= 505*1009 - 504 *1009
=1009*( 505-504)= 1009
d) (-3-9-15-...-33 ) +(6+12+...+36)= S
(-3-9-15-...-33 )= -3 (1+3+5+7+9+ 11) = (-3) *6*6 ( formula este nxn
n = (ultimul termen + primul ):2 sau nr de termeni
(6+12+...+36)=6 *(1+2+...+6)= 6*6*7:2= 3*6*7
S= 3*6*7- 3*6*6= 3*6(7-6)= 3*6=18
