S-r-12-12r-1-12r-2-12r-3-12r-4-with-1-lt-r-lt-1-If-S-a-S-a-2016-with-1-lt-a-lt-1-What-is-the-value-of-S-a-S-a-

Question Number 9484 by Joel575 last updated on 10/Dec/16

S (r) = 12 + 12 r^{1} + 12 r^{2} + 12 r^{3} + 12 r^{4} + \dots

with - 1 < r < 1

If S (a) . S (- a) = 2016, with - 1 < a < 1

What is the value of S (a) + S (- a) ?

Answered by mrW last updated on 10/Dec/16

S (r) = \frac{12}{1 - r}

S (a) = \frac{12}{1 - a}

S (- a) = \frac{12}{1 + a}

S (a) \cdot S (- a) = \frac{12}{1 - a} \times \frac{12}{1 + a} = 2016

\frac{144}{1 - a^{2}} = 2016

\frac{1}{1 - a^{2}} = \frac{2016}{144} = 14

a = \pm \sqrt{\frac{13}{14}}

S (a) + S (- a) = \frac{12}{1 - a} + \frac{12}{1 + a} = \frac{24}{1 - a^{2}}

= 24 \times 14 = 336

Commented by Joel575 last updated on 11/Dec/16

t h a n k y o u v e r y m u c h

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