Solve i+A_{1}(1+1/3)(1+1/3^2)(1+1/3^4)(1+1/3^8)(1+frac{1}{3^16})=

$$i + A _ { 1 } ( 1 + \frac { 1 } { 3 } ) ( 1 + \frac { 1 } { 3 ^ { 2 } } ) ( 1 + \frac { 1 } { 3 ^ { 4 } } ) ( 1 + \frac { 1 } { 3 ^ { 8 } } ) ( 1 + \frac { 1 } { 3 ^ { 16 } } ) =$$

Evaluate

$$\frac{926510094425920A_{1}}{617673396283947}+i$$

Solution Steps

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

$$i+A_{1}\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{3+1}{3}\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Add 3 and 1 to get 4.

$$i+A_{1}\times \frac{4}{3}\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Calculate 3 to the power of 2 and get 9.

$$i+A_{1}\times \frac{4}{3}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{4}{3}\left(\frac{9}{9}+\frac{1}{9}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{4}{3}\times \frac{9+1}{9}\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Add 9 and 1 to get 10.

$$i+A_{1}\times \frac{4}{3}\times \frac{10}{9}\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{4\times 10}{3\times 9}\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{40}{27}\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Calculate 3 to the power of 4 and get 81.

$$i+A_{1}\times \frac{40}{27}\left(1+\frac{1}{81}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{40}{27}\left(\frac{81}{81}+\frac{1}{81}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{40}{27}\times \frac{81+1}{81}\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Add 81 and 1 to get 82.

$$i+A_{1}\times \frac{40}{27}\times \frac{82}{81}\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{40\times 82}{27\times 81}\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{3280}{2187}\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Calculate 3 to the power of 8 and get 6561.

$$i+A_{1}\times \frac{3280}{2187}\left(1+\frac{1}{6561}\right)\left(1+\frac{1}{3^{16}}\right)$$

Convert 1 to fraction \frac{6561}{6561}.

$$i+A_{1}\times \frac{3280}{2187}\left(\frac{6561}{6561}+\frac{1}{6561}\right)\left(1+\frac{1}{3^{16}}\right)$$

Since \frac{6561}{6561} and \frac{1}{6561} have the same denominator, add them by adding their numerators.

$$i+A_{1}\times \frac{3280}{2187}\times \frac{6561+1}{6561}\left(1+\frac{1}{3^{16}}\right)$$

Add 6561 and 1 to get 6562.

$$i+A_{1}\times \frac{3280}{2187}\times \frac{6562}{6561}\left(1+\frac{1}{3^{16}}\right)$$

Multiply \frac{3280}{2187} times \frac{6562}{6561} by multiplying numerator times numerator and denominator times denominator.

$$i+A_{1}\times \frac{3280\times 6562}{2187\times 6561}\left(1+\frac{1}{3^{16}}\right)$$

Do the multiplications in the fraction \frac{3280\times 6562}{2187\times 6561}.

$$i+A_{1}\times \frac{21523360}{14348907}\left(1+\frac{1}{3^{16}}\right)$$

Calculate 3 to the power of 16 and get 43046721.

$$i+A_{1}\times \frac{21523360}{14348907}\left(1+\frac{1}{43046721}\right)$$

Convert 1 to fraction \frac{43046721}{43046721}.

$$i+A_{1}\times \frac{21523360}{14348907}\left(\frac{43046721}{43046721}+\frac{1}{43046721}\right)$$

Since \frac{43046721}{43046721} and \frac{1}{43046721} have the same denominator, add them by adding their numerators.

$$i+A_{1}\times \frac{21523360}{14348907}\times \frac{43046721+1}{43046721}$$

Add 43046721 and 1 to get 43046722.

$$i+A_{1}\times \frac{21523360}{14348907}\times \frac{43046722}{43046721}$$

Multiply \frac{21523360}{14348907} times \frac{43046722}{43046721} by multiplying numerator times numerator and denominator times denominator.

$$i+A_{1}\times \frac{21523360\times 43046722}{14348907\times 43046721}$$

Do the multiplications in the fraction \frac{21523360\times 43046722}{14348907\times 43046721}.

$$i+A_{1}\times \frac{926510094425920}{617673396283947}$$

Expand

$$\frac{926510094425920A_{1}}{617673396283947}+i$$

Solution Steps

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

$$i+A_{1}\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{3+1}{3}\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Add 3 and 1 to get 4.

$$i+A_{1}\times \frac{4}{3}\left(1+\frac{1}{3^{2}}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Calculate 3 to the power of 2 and get 9.

$$i+A_{1}\times \frac{4}{3}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{4}{3}\left(\frac{9}{9}+\frac{1}{9}\right)\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{4}{3}\times \frac{9+1}{9}\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Add 9 and 1 to get 10.

$$i+A_{1}\times \frac{4}{3}\times \frac{10}{9}\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{4\times 10}{3\times 9}\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{40}{27}\left(1+\frac{1}{3^{4}}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Calculate 3 to the power of 4 and get 81.

$$i+A_{1}\times \frac{40}{27}\left(1+\frac{1}{81}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{40}{27}\left(\frac{81}{81}+\frac{1}{81}\right)\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{40}{27}\times \frac{81+1}{81}\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Add 81 and 1 to get 82.

$$i+A_{1}\times \frac{40}{27}\times \frac{82}{81}\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{40\times 82}{27\times 81}\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

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

$$i+A_{1}\times \frac{3280}{2187}\left(1+\frac{1}{3^{8}}\right)\left(1+\frac{1}{3^{16}}\right)$$

Calculate 3 to the power of 8 and get 6561.

$$i+A_{1}\times \frac{3280}{2187}\left(1+\frac{1}{6561}\right)\left(1+\frac{1}{3^{16}}\right)$$

Convert 1 to fraction \frac{6561}{6561}.

$$i+A_{1}\times \frac{3280}{2187}\left(\frac{6561}{6561}+\frac{1}{6561}\right)\left(1+\frac{1}{3^{16}}\right)$$

Since \frac{6561}{6561} and \frac{1}{6561} have the same denominator, add them by adding their numerators.

$$i+A_{1}\times \frac{3280}{2187}\times \frac{6561+1}{6561}\left(1+\frac{1}{3^{16}}\right)$$

Add 6561 and 1 to get 6562.

$$i+A_{1}\times \frac{3280}{2187}\times \frac{6562}{6561}\left(1+\frac{1}{3^{16}}\right)$$

Multiply \frac{3280}{2187} times \frac{6562}{6561} by multiplying numerator times numerator and denominator times denominator.

$$i+A_{1}\times \frac{3280\times 6562}{2187\times 6561}\left(1+\frac{1}{3^{16}}\right)$$

Do the multiplications in the fraction \frac{3280\times 6562}{2187\times 6561}.

$$i+A_{1}\times \frac{21523360}{14348907}\left(1+\frac{1}{3^{16}}\right)$$

Calculate 3 to the power of 16 and get 43046721.

$$i+A_{1}\times \frac{21523360}{14348907}\left(1+\frac{1}{43046721}\right)$$

Convert 1 to fraction \frac{43046721}{43046721}.

$$i+A_{1}\times \frac{21523360}{14348907}\left(\frac{43046721}{43046721}+\frac{1}{43046721}\right)$$

Since \frac{43046721}{43046721} and \frac{1}{43046721} have the same denominator, add them by adding their numerators.

$$i+A_{1}\times \frac{21523360}{14348907}\times \frac{43046721+1}{43046721}$$

Add 43046721 and 1 to get 43046722.

$$i+A_{1}\times \frac{21523360}{14348907}\times \frac{43046722}{43046721}$$

Multiply \frac{21523360}{14348907} times \frac{43046722}{43046721} by multiplying numerator times numerator and denominator times denominator.

$$i+A_{1}\times \frac{21523360\times 43046722}{14348907\times 43046721}$$

Do the multiplications in the fraction \frac{21523360\times 43046722}{14348907\times 43046721}.

$$i+A_{1}\times \frac{926510094425920}{617673396283947}$$