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How do you find the sum of the infinite geometric series -3, -3/2, -3/4, -3/8?

1 Answer

Nov 21, 2015

The sum of this sequence is $- 6$ $-6$

Explanation:

To find the sum of an infinite geometric sequence we use the formula:

$S = \frac{a_{1}}{1 - q}$ $S=a_1/(1-q)$

First we have to find $q$ $q$ to see if the sequence is convergent:

$q = - \frac{3}{2} : (- 3) = \frac{1}{2}$ $q=-3/2:(-3)=1/2$

$| q | < 1$ $abs(q)<1$ , so the sequence is convergent. We can calculate the sum:

$S = \frac{a_{1}}{1 - q} = \frac{- 3}{1 - \frac{1}{2}} = - \frac{3}{\frac{1}{2}} = - 3 \cdot 2 = - 6$ $S=a_1/(1-q)=(-3)/(1-1/2)=-3/(1/2)=-3*2=-6$

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