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# expressing my answer as an exact value in fraction form for a geometric series?

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so I'm given a geometric series where $${t_1 = 6}$$ and $${r = 1.5}$$, where $${t_1}$$ is the first term and $${r}$$ is the common ratio.

i want to use the formula $$S_n = {t_1 ( 1 - r^{n}) \over 1 - r}$$ where $${S_n}$$ is the sum of the first $${n}$$ terms and $${n}$$ is the number of terms.

I want to find the sum for the first 10 terms. i plugged my numbers in and got the textbook answer of $${679.98}$$ by doing bedmas on my calculator since there were big numbers.

the text also wants me to express my answer as an exact value in fraction form, how should i do that? the textbook answer is $${174 075 \over 256}$$

Guest Jul 6, 2018
edited by Guest  Jul 6, 2018
edited by Guest  Jul 6, 2018
#1
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Sum=6 x [1 - 1.5^10] / [1 - 1.5]

Sum=6 x [1 -  57.665] / [-0.5]

Sum=6 x [-56.665] / [-0.5]

Sum =6 x   -56.6650390625 / - 0.5

Sum =-339.990234375 / -0.5

Guest Jul 6, 2018
#2
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the textbook answer is $${174075 \over 256}$$ as the exact value in fraction form though :")

Guest Jul 6, 2018
#3
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-339.990234375 / -0.5  x 512/512

174,075 / 256

Guest Jul 6, 2018