Solve =1+0.3+frac{(0.3)^{2}}{2}+(0.3)^3/3+(0.3)^4/8+(0.3)^5/15+(0.3)^6/48

$$= 1 + 0.3 + \frac { ( 0.3 ) ^ { 2 } } { 2 } + \frac { ( 0.3 ) ^ { 3 } } { 3 } + \frac { ( 0.3 ) ^ { 4 } } { 8 } + \frac { ( 0.3 ) ^ { 5 } } { 15 } + \frac { ( 0.3 ) ^ { 6 } } { 48 }$$

Evaluate

$$1.3551896875$$

Solution Steps

Add 1 and 0.3 to get 1.3.

$$1.3+\frac{0.3^{2}}{2}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$1.3+\frac{0.09}{2}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$1.3+\frac{9}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{13}{10}+\frac{9}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{260}{200}+\frac{9}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{260+9}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

Add 260 and 9 to get 269.

$$\frac{269}{200}+\frac{0.3^{3}}{3}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

Calculate 0.3 to the power of 3 and get 0.027.

$$\frac{269}{200}+\frac{0.027}{3}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{269}{200}+\frac{27}{3000}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{269}{200}+\frac{9}{1000}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{1345}{1000}+\frac{9}{1000}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{1345+9}{1000}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

Add 1345 and 9 to get 1354.

$$\frac{1354}{1000}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{677}{500}+\frac{0.3^{4}}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

Calculate 0.3 to the power of 4 and get 0.0081.

$$\frac{677}{500}+\frac{0.0081}{8}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{677}{500}+\frac{81}{80000}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{108320}{80000}+\frac{81}{80000}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

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

$$\frac{108320+81}{80000}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

Add 108320 and 81 to get 108401.

$$\frac{108401}{80000}+\frac{0.3^{5}}{15}+\frac{0.3^{6}}{48}$$

Calculate 0.3 to the power of 5 and get 0.00243.

$$\frac{108401}{80000}+\frac{0.00243}{15}+\frac{0.3^{6}}{48}$$

Expand \frac{0.00243}{15} by multiplying both numerator and the denominator by 100000.

$$\frac{108401}{80000}+\frac{243}{1500000}+\frac{0.3^{6}}{48}$$

Reduce the fraction \frac{243}{1500000} to lowest terms by extracting and canceling out 3.

$$\frac{108401}{80000}+\frac{81}{500000}+\frac{0.3^{6}}{48}$$

Least common multiple of 80000 and 500000 is 2000000. Convert \frac{108401}{80000} and \frac{81}{500000} to fractions with denominator 2000000.

$$\frac{2710025}{2000000}+\frac{324}{2000000}+\frac{0.3^{6}}{48}$$

Since \frac{2710025}{2000000} and \frac{324}{2000000} have the same denominator, add them by adding their numerators.

$$\frac{2710025+324}{2000000}+\frac{0.3^{6}}{48}$$

Add 2710025 and 324 to get 2710349.

$$\frac{2710349}{2000000}+\frac{0.3^{6}}{48}$$

Calculate 0.3 to the power of 6 and get 0.000729.

$$\frac{2710349}{2000000}+\frac{0.000729}{48}$$

Expand \frac{0.000729}{48} by multiplying both numerator and the denominator by 1000000.

$$\frac{2710349}{2000000}+\frac{729}{48000000}$$

Reduce the fraction \frac{729}{48000000} to lowest terms by extracting and canceling out 3.

$$\frac{2710349}{2000000}+\frac{243}{16000000}$$

Least common multiple of 2000000 and 16000000 is 16000000. Convert \frac{2710349}{2000000} and \frac{243}{16000000} to fractions with denominator 16000000.

$$\frac{21682792}{16000000}+\frac{243}{16000000}$$

Since \frac{21682792}{16000000} and \frac{243}{16000000} have the same denominator, add them by adding their numerators.

$$\frac{21682792+243}{16000000}$$

Add 21682792 and 243 to get 21683035.

$$\frac{21683035}{16000000}$$

Reduce the fraction \frac{21683035}{16000000} to lowest terms by extracting and canceling out 5.

$$\frac{4336607}{3200000}$$

Factor

$$\frac{11 \cdot 263 \cdot 1499}{2 ^ {10} \cdot 5 ^ {5}} = 1\frac{1136607}{3200000} = 1.3551896875$$