Question

x=1+3+5+...+2013 aratati ca e patrat perfect.

Answer 1

X = 1+(1+2*1) + (1+2*2) + (1+2*3) + ... + (1+2*1006)

Suma din enunț are deci 1007 termeni.

X = 1*1007 + 2(1+2+3+...+1006) = 1007 + 2*1006*1007 / 2 = 1007(1+1006) = 1007².

Pentru suma 1+2+3+...+1006 am folosit formula lui Gauss. O știai, nu ?

Simplu, nu ?

Green eyes.

Answer 2

x=1+3+5+...+2013
x= (2-1)+(4-1)+(6-1)+...+(2014-1)
x= 2+4+6+...+2014 - 1×2014/2
x=2×(1+2+3+...+1007) - 1007
x= 2× 1007×1008/2 -1007
x= 1007×1008 - 1007
x= 1007× ( 1008-1)
x= 1007×1007
x= 1007^2 este patrat perfect