Solucionar D(3)=(1/9+1)^2*1/3+(1/9)*1/3+(frac{1}{9}-1)^2*frac{2}{9}+(frac{1}{9}-2)*frac{1}{9}

$$D ( 3 ) = ( \frac { 1 } { 9 } + 1 ) ^ { 2 } \times \frac { 1 } { 3 } + ( \frac { 1 } { 9 } ) \times \frac { 1 } { 3 } + ( \frac { 1 } { 9 } - 1 ) ^ { 2 } \times \frac { 2 } { 9 } + ( \frac { 1 } { 9 } - 2 ) \times \frac { 1 } { 9 }$$

Calcular

$$\frac{302}{729}\approx 0,414266118$$

Pasos de la solución

Suma \frac{1}{9} y 1 para obtener \frac{10}{9}.

$$\left(\frac{10}{9}\right)^{2}\times \frac{1}{3}+\frac{1}{9}\times \frac{1}{3}+\left(\frac{1}{9}-1\right)^{2}\times \frac{2}{9}+\left(\frac{1}{9}-2\right)\times \frac{1}{9}$$

Calcula \frac{10}{9} a la potencia de 2 y obtiene \frac{100}{81}.

$$\frac{100}{81}\times \frac{1}{3}+\frac{1}{9}\times \frac{1}{3}+\left(\frac{1}{9}-1\right)^{2}\times \frac{2}{9}+\left(\frac{1}{9}-2\right)\times \frac{1}{9}$$

Multiplica \frac{100}{81} y \frac{1}{3} para obtener \frac{100}{243}.

$$\frac{100}{243}+\frac{1}{9}\times \frac{1}{3}+\left(\frac{1}{9}-1\right)^{2}\times \frac{2}{9}+\left(\frac{1}{9}-2\right)\times \frac{1}{9}$$

Multiplica \frac{1}{9} y \frac{1}{3} para obtener \frac{1}{27}.

$$\frac{100}{243}+\frac{1}{27}+\left(\frac{1}{9}-1\right)^{2}\times \frac{2}{9}+\left(\frac{1}{9}-2\right)\times \frac{1}{9}$$

Suma \frac{100}{243} y \frac{1}{27} para obtener \frac{109}{243}.

$$\frac{109}{243}+\left(\frac{1}{9}-1\right)^{2}\times \frac{2}{9}+\left(\frac{1}{9}-2\right)\times \frac{1}{9}$$

Resta 1 de \frac{1}{9} para obtener -\frac{8}{9}.

$$\frac{109}{243}+\left(-\frac{8}{9}\right)^{2}\times \frac{2}{9}+\left(\frac{1}{9}-2\right)\times \frac{1}{9}$$

Calcula -\frac{8}{9} a la potencia de 2 y obtiene \frac{64}{81}.

$$\frac{109}{243}+\frac{64}{81}\times \frac{2}{9}+\left(\frac{1}{9}-2\right)\times \frac{1}{9}$$

Multiplica \frac{64}{81} y \frac{2}{9} para obtener \frac{128}{729}.

$$\frac{109}{243}+\frac{128}{729}+\left(\frac{1}{9}-2\right)\times \frac{1}{9}$$

Suma \frac{109}{243} y \frac{128}{729} para obtener \frac{455}{729}.

$$\frac{455}{729}+\left(\frac{1}{9}-2\right)\times \frac{1}{9}$$

Resta 2 de \frac{1}{9} para obtener -\frac{17}{9}.

$$\frac{455}{729}-\frac{17}{9}\times \frac{1}{9}$$

Multiplica -\frac{17}{9} y \frac{1}{9} para obtener -\frac{17}{81}.

$$\frac{455}{729}-\frac{17}{81}$$

Resta \frac{17}{81} de \frac{455}{729} para obtener \frac{302}{729}.

$$\frac{302}{729}$$

Factorizar

$$\frac{2 \cdot 151}{3 ^ {6}} = 0,41426611796982166$$