Question

Stabiliți paritatea sumelor:
a Si= 2 +4 +6+ ... +198;
b S2 = 1 + 3 + 5 + ... +175;
c Sz = 5 + 9 +13 + ... + 101;
d S4= 5 + 10 + 15 + ... + 85.

Answer 1

Explicație pas cu pas:

S1= 2*(1+2+...+99)=2*(99*100)÷2=99*100=9900

S2=(1+2+3+....+175)-(2+4+6+...+174)=175*176÷2-2*(1+2+3+....+87)= 30800÷2-2*87*88÷2=15400-7656=7744

S3=(1+4)+(2+4)+....+(97+4)=4*97 + (1+2+...+97)= 388+97*98÷2=388+4753=5141

S4=5*(1+2+....+17)=5*17*18÷2=765