Solve -1000+372.5/1.28+372.5/1.28^2+372.5/1.28^3+372.5/1.28^4+frac{672.5}{1.28^5}

$$-1000+ \frac{ 372.5 }{ 1.28 } + \frac{ 372.5 }{ { 1.28 }^{ 2 } } + \frac{ 372.5 }{ { 1.28 }^{ 3 } } + \frac{ 372.5 }{ { 1.28 }^{ 4 } } + \frac{ 672.5 }{ { 1.28 }^{ 5 } }$$

Evaluate

$$30.48374690115451812744140625$$

Solution Steps

Expand \frac{372.5}{1.28} by multiplying both numerator and the denominator by 100.

$$-1000+\frac{37250}{128}+\frac{372.5}{1.28^{2}}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Reduce the fraction \frac{37250}{128} to lowest terms by extracting and canceling out 2.

$$-1000+\frac{18625}{64}+\frac{372.5}{1.28^{2}}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Convert -1000 to fraction -\frac{64000}{64}.

$$-\frac{64000}{64}+\frac{18625}{64}+\frac{372.5}{1.28^{2}}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Since -\frac{64000}{64} and \frac{18625}{64} have the same denominator, add them by adding their numerators.

$$\frac{-64000+18625}{64}+\frac{372.5}{1.28^{2}}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Add -64000 and 18625 to get -45375.

$$-\frac{45375}{64}+\frac{372.5}{1.28^{2}}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Calculate 1.28 to the power of 2 and get 1.6384.

$$-\frac{45375}{64}+\frac{372.5}{1.6384}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Expand \frac{372.5}{1.6384} by multiplying both numerator and the denominator by 10000.

$$-\frac{45375}{64}+\frac{3725000}{16384}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Reduce the fraction \frac{3725000}{16384} to lowest terms by extracting and canceling out 8.

$$-\frac{45375}{64}+\frac{465625}{2048}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Least common multiple of 64 and 2048 is 2048. Convert -\frac{45375}{64} and \frac{465625}{2048} to fractions with denominator 2048.

$$-\frac{1452000}{2048}+\frac{465625}{2048}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Since -\frac{1452000}{2048} and \frac{465625}{2048} have the same denominator, add them by adding their numerators.

$$\frac{-1452000+465625}{2048}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Add -1452000 and 465625 to get -986375.

$$-\frac{986375}{2048}+\frac{372.5}{1.28^{3}}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Calculate 1.28 to the power of 3 and get 2.097152.

$$-\frac{986375}{2048}+\frac{372.5}{2.097152}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Expand \frac{372.5}{2.097152} by multiplying both numerator and the denominator by 1000000.

$$-\frac{986375}{2048}+\frac{372500000}{2097152}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Reduce the fraction \frac{372500000}{2097152} to lowest terms by extracting and canceling out 32.

$$-\frac{986375}{2048}+\frac{11640625}{65536}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Least common multiple of 2048 and 65536 is 65536. Convert -\frac{986375}{2048} and \frac{11640625}{65536} to fractions with denominator 65536.

$$-\frac{31564000}{65536}+\frac{11640625}{65536}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Since -\frac{31564000}{65536} and \frac{11640625}{65536} have the same denominator, add them by adding their numerators.

$$\frac{-31564000+11640625}{65536}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Add -31564000 and 11640625 to get -19923375.

$$-\frac{19923375}{65536}+\frac{372.5}{1.28^{4}}+\frac{672.5}{1.28^{5}}$$

Calculate 1.28 to the power of 4 and get 2.68435456.

$$-\frac{19923375}{65536}+\frac{372.5}{2.68435456}+\frac{672.5}{1.28^{5}}$$

Expand \frac{372.5}{2.68435456} by multiplying both numerator and the denominator by 100000000.

$$-\frac{19923375}{65536}+\frac{37250000000}{268435456}+\frac{672.5}{1.28^{5}}$$

Reduce the fraction \frac{37250000000}{268435456} to lowest terms by extracting and canceling out 128.

$$-\frac{19923375}{65536}+\frac{291015625}{2097152}+\frac{672.5}{1.28^{5}}$$

Least common multiple of 65536 and 2097152 is 2097152. Convert -\frac{19923375}{65536} and \frac{291015625}{2097152} to fractions with denominator 2097152.

$$-\frac{637548000}{2097152}+\frac{291015625}{2097152}+\frac{672.5}{1.28^{5}}$$

Since -\frac{637548000}{2097152} and \frac{291015625}{2097152} have the same denominator, add them by adding their numerators.

$$\frac{-637548000+291015625}{2097152}+\frac{672.5}{1.28^{5}}$$

Add -637548000 and 291015625 to get -346532375.

$$-\frac{346532375}{2097152}+\frac{672.5}{1.28^{5}}$$

Calculate 1.28 to the power of 5 and get 3.4359738368.

$$-\frac{346532375}{2097152}+\frac{672.5}{3.4359738368}$$

Expand \frac{672.5}{3.4359738368} by multiplying both numerator and the denominator by 10000000000.

$$-\frac{346532375}{2097152}+\frac{6725000000000}{34359738368}$$

Reduce the fraction \frac{6725000000000}{34359738368} to lowest terms by extracting and canceling out 512.

$$-\frac{346532375}{2097152}+\frac{13134765625}{67108864}$$

Least common multiple of 2097152 and 67108864 is 67108864. Convert -\frac{346532375}{2097152} and \frac{13134765625}{67108864} to fractions with denominator 67108864.

$$-\frac{11089036000}{67108864}+\frac{13134765625}{67108864}$$

Since -\frac{11089036000}{67108864} and \frac{13134765625}{67108864} have the same denominator, add them by adding their numerators.

$$\frac{-11089036000+13134765625}{67108864}$$

Add -11089036000 and 13134765625 to get 2045729625.

$$\frac{2045729625}{67108864}$$

Factor

$$\frac{3 \cdot 157 \cdot 34747 \cdot 5 ^ {3}}{2 ^ {26}} = 30\frac{32463705}{67108864} = 30.483746901154518$$