3 la puterea n×3la puterea n+1×3la puterea n+2

Răspuns :

[tex] {3}^{n} \times {3}^{n + 1} \times {3}^{n + 2} = {3}^{n + n + 1 + n + 2} [/tex]

[tex] = {3}^{3n + 3} = {3}^{3(n + 1)} = {27}^{n + 1} [/tex]

[tex]{2}^{1} \times {2}^{2} \times \: ... \:\times {2}^{20}[/tex]

[tex]={2}^{1+2+...+20}[/tex]

[tex]={2}^{\frac{20(20+1)}{2}}[/tex]

[tex]={2}^{\frac{20 \times 21}{2}}[/tex]

[tex]={2}^{10×21}[/tex]

[tex]={2}^{210}[/tex]

Formulă :

[tex]1+2+...+n=\frac{n(n+1)}{2}[/tex]