Question

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

Answer 1

${3}^{n} \times {3}^{n + 1} \times {3}^{n + 2} = {3}^{n + n + 1 + n + 2}$

$= {3}^{3n + 3} = {3}^{3(n + 1)} = {27}^{n + 1}$

${2}^{1} \times {2}^{2} \times \: ... \:\times {2}^{20}$

$={2}^{1+2+...+20}$

$={2}^{\frac{20(20+1)}{2}}$

$={2}^{\frac{20 \times 21}{2}}$

$={2}^{10×21}$

$={2}^{210}$

Formulă :

$1+2+...+n=\frac{n(n+1)}{2}$