Question

stabiliti daca: n=36*1+36*3.......+36*999 este patrat perfect.Vreau rezolvare pentru clasa a v-a!!!!

Answer 1

36x(1++3+5+....9999)
       1+2+3+4+5+.....+1000= 1000*1001:2 =500*1001
   -   2+4+6+8+  1000         = 2x(500x501/2)   =500*501

deci avem 
36x  {(500x1001)-(500x501)}

{(500x1001)-(500x501)}
500x(1001-501)=500x500

Total  36x500x500  patrat????
da pentru ca

36x500x500  =6²x500²