Question

Scrieți numărul a ca pătrat perfect al unui număr natural unde : a = 1 + 3 + 5 +. . . + 49

Answer 1

3-1=2
nr termeni (49-1):2+1=24+1=25
a = 1 + 3 + 5 +. . . + 49 =
=1+(1+2)+(1+4)+...+(1+48)=
=1×25+2+4+...+48=
=25+2(1+2+...+24)/2=
=25+2×24×25/2=
=25+24×25=
=25(1+24)=
=25×25=25²

Answer 2

(2×0+1)+(2×1+1)+(2×2+1)+...+(2×24+1)=
2(1+2+...+24) + 1+1+1+....+1=
2(24+25) ÷ 2 +25=
24+25+25=
25(24+1)=
25×25=
a=25 la a doua.