Solve left(1+1/3right)left(1+1/3^2right)left(1+1/3^4right)

$$\left( 1+ \frac{ 1 }{ 3 } \right) \left( 1+ \frac{ 1 }{ { 3 }^{ 2 } } \right) \left( 1+ \frac{ 1 }{ { 3 }^{ 4 } } \right)$$

Evaluate

$$\frac{3280}{2187}\approx 1.499771376$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{3}\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)$$

Add 3 and 1 to get 4.

$$\frac{4}{3}\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4}{3}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{3^{4}}\right)$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{4}{3}\left(\frac{9}{9}+\frac{1}{9}\right)\left(1+\frac{1}{3^{4}}\right)$$

Since \frac{9}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{4}{3}\times \frac{9+1}{9}\left(1+\frac{1}{3^{4}}\right)$$

Add 9 and 1 to get 10.

$$\frac{4}{3}\times \frac{10}{9}\left(1+\frac{1}{3^{4}}\right)$$

Multiply \frac{4}{3} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 10}{3\times 9}\left(1+\frac{1}{3^{4}}\right)$$

Do the multiplications in the fraction \frac{4\times 10}{3\times 9}.

$$\frac{40}{27}\left(1+\frac{1}{3^{4}}\right)$$

Calculate 3 to the power of 4 and get 81.

$$\frac{40}{27}\left(1+\frac{1}{81}\right)$$

Convert 1 to fraction \frac{81}{81}.

$$\frac{40}{27}\left(\frac{81}{81}+\frac{1}{81}\right)$$

Since \frac{81}{81} and \frac{1}{81} have the same denominator, add them by adding their numerators.

$$\frac{40}{27}\times \frac{81+1}{81}$$

Add 81 and 1 to get 82.

$$\frac{40}{27}\times \frac{82}{81}$$

Multiply \frac{40}{27} times \frac{82}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{40\times 82}{27\times 81}$$

Do the multiplications in the fraction \frac{40\times 82}{27\times 81}.

$$\frac{3280}{2187}$$

Factor

$$\frac{2 ^ {4} \cdot 5 \cdot 41}{3 ^ {7}} = 1\frac{1093}{2187} = 1.4997713763145861$$