Solve =1+0.3+(0.3)^2/2+(0.3)^3/3+(0.3)^4/8

$$= 1 + 0.3 + \frac { ( 0.3 ) ^ { 2 } } { 2 } + \frac { ( 0.3 ) ^ { 3 } } { 3 } + \frac { ( 0.3 ) ^ { 4 } } { 8 }$$

Evaluate

$$1.3550125$$

Solution Steps

Add 1 and 0.3 to get 1.3.

$$1.3+\frac{0.3^{2}}{2}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$1.3+\frac{0.09}{2}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}$$

Expand \frac{0.09}{2} by multiplying both numerator and the denominator by 100.

$$1.3+\frac{9}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}$$

Convert decimal number 1.3 to fraction \frac{13}{10}.

$$\frac{13}{10}+\frac{9}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}$$

Least common multiple of 10 and 200 is 200. Convert \frac{13}{10} and \frac{9}{200} to fractions with denominator 200.

$$\frac{260}{200}+\frac{9}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}$$

Since \frac{260}{200} and \frac{9}{200} have the same denominator, add them by adding their numerators.

$$\frac{260+9}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}$$

Add 260 and 9 to get 269.

$$\frac{269}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}$$

Calculate 0.3 to the power of 3 and get 0.027.

$$\frac{269}{200}+\frac{0.027}{3}+\frac{0.3^{4}}{8}$$

Expand \frac{0.027}{3} by multiplying both numerator and the denominator by 1000.

$$\frac{269}{200}+\frac{27}{3000}+\frac{0.3^{4}}{8}$$

Reduce the fraction \frac{27}{3000} to lowest terms by extracting and canceling out 3.

$$\frac{269}{200}+\frac{9}{1000}+\frac{0.3^{4}}{8}$$

Least common multiple of 200 and 1000 is 1000. Convert \frac{269}{200} and \frac{9}{1000} to fractions with denominator 1000.

$$\frac{1345}{1000}+\frac{9}{1000}+\frac{0.3^{4}}{8}$$

Since \frac{1345}{1000} and \frac{9}{1000} have the same denominator, add them by adding their numerators.

$$\frac{1345+9}{1000}+\frac{0.3^{4}}{8}$$

Add 1345 and 9 to get 1354.

$$\frac{1354}{1000}+\frac{0.3^{4}}{8}$$

Reduce the fraction \frac{1354}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{677}{500}+\frac{0.3^{4}}{8}$$

Calculate 0.3 to the power of 4 and get 0.0081.

$$\frac{677}{500}+\frac{0.0081}{8}$$

Expand \frac{0.0081}{8} by multiplying both numerator and the denominator by 10000.

$$\frac{677}{500}+\frac{81}{80000}$$

Least common multiple of 500 and 80000 is 80000. Convert \frac{677}{500} and \frac{81}{80000} to fractions with denominator 80000.

$$\frac{108320}{80000}+\frac{81}{80000}$$

Since \frac{108320}{80000} and \frac{81}{80000} have the same denominator, add them by adding their numerators.

$$\frac{108320+81}{80000}$$

Add 108320 and 81 to get 108401.

$$\frac{108401}{80000}$$

Factor

$$\frac{108401}{2 ^ {7} \cdot 5 ^ {4}} = 1\frac{28401}{80000} = 1.3550125$$