Question

Calculati:
S=8+16+24+32+.......+800
Arătați ca nr.
a=2×(1+2+3+4+......2010)+2011 este pătrat perfect.

Answer 1

[tex]S = 8+16+24+...+800 = 8 \left( 1 + 2 + 3 + ... + 100\right) = 8 \sum\limits_{k=1}^{100}k \\\\ = 8 \cdot \frac{100\cdot101}{2}=40400[/tex]

$a = 2\left ( 1+2+3+...+2010\right)+2011 = 2 \cdot \frac{2010*2011}{2}+2011 \\ = 2010 \cdot 2011 + 2011 = 2011 \cdot 2011 = 2011^2$