Question

aflati numarul natural al carui patrat perfect este suma 1+3+5+...+35

Answer 1

1+3+5+...+35=
=2*0+1+2*1+1+2*2+1+..+2*17+1=
=2(0+1+2+3+..+17)+1+1+1+..+1 (de 18 ori)=
=2*17*18/2+18=
=17*18+18=
=18(17+1)=
=18*18=18^2

Answer 2

Vom folosi formula:

$\it 1+3+5+\ ...\ +2n-1 =n^2$

Pentru  suma dată, 2n-1 = 35 ⇒ 2n=36 ⇒ n = 18.

Prin urmare, vom avea:

$\it 1+3+5+\ ...\ +35 = 18^2= 324$