Question

Fie numarul A= 16+48+80+......+1584. Radacina patrata a sa este .....?​

Answer 1

Răspuns:

16(1+3+5+....+99)

Nt=( ultimu numar- primul numar) :din cat se repet numerele+1

Nt=(99-1):2+1=50

S=(ultimul numar +primul numar) Nt/2

$16 \times \frac{(99 + 1)50}{2}$

16×50×50

$\sqrt{16} \times \sqrt{50 {}^{2} }$

4×50=200

Answer 2

Răspuns:

Explicație pas cu pas:

A= 16+48+80+......+1584=16(1+3+5+.......+99)   suma de nr impare

Daca revenim la Suma Gauss

1+3+5+..+99=(1+2+3+....+100)-(2+4+6+....+100)=(1+2+3+...+100)-2(1+2+3+....+50)=

100×101/2-2×50×51/2=50×101-50×51=50(101-51)=50×50=50²

A=16×50²=4²×50²

√A=4×50=200