Solve (1+1/2)(1+1/2^2)

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

Evaluate

$$\frac{15}{8}=1.875$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

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

Calculate 2 to the power of 2 and get 4.

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

Convert 1 to fraction \frac{4}{4}.

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

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}\times \frac{4+1}{4}$$

Add 4 and 1 to get 5.

$$\frac{3}{2}\times \frac{5}{4}$$

Multiply \frac{3}{2} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 5}{2\times 4}$$

Do the multiplications in the fraction \frac{3\times 5}{2\times 4}.

$$\frac{15}{8}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {3}} = 1\frac{7}{8} = 1.875$$