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Find the sum of the series. Enter the exact answer.

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- 4 + 1 - 1/4 + 1/16 - 1/64 + 1/256 - ... =

asked Dec 13, 2014 in PRECALCULUS by anonymous

1 Answer

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The series - 4 + 1 - 1/4 + 1/16 - 1/64 + 1/256 - ...

Above series is geometric series.

Common ratio r = t₂/t₁

r = 1/(- 4)

r = - 1/4

In this case r < 1.

Formula for the sum of the sequence Sn = a(1 - rn)/(1 - r)

Where r is common ratio. a is first term.

Substitute r = (- 1/4) and a = - 4 in Sn .

Sn = [(- 4)(1 - (- 1/4)n]/[1 - (- 1/4)]

Sn = [(- 4)(1 - (- 0.25)n]/[1 - (- 0.25)]

Sn = [(- 4)(1 - (- 0.25)n]/[1 + 0.25]

Sn = (- 4 + 4 (- 0.25)n)/1.25

    = 3.2 (- 1 + (- 0.25)n)

answered Dec 13, 2014 by david Expert
edited Dec 13, 2014 by bradely

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