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How do you find the sum of the infinite geometric series -10,-5,-5/2?

Answer 1

Serenity Johnson

Sum #=-20#

The formula #S_oo=a_1/(1-r)#

#a_1=-10# and #r=1/2#

#S_oo=-10/(1-1/2)#

#S_oo=-20#

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Answer 2

Elijah Allen

To find the sum of an infinite geometric series, use the formula:

[ S = \frac{a}{1 - r} ]

where ( a ) is the first term and ( r ) is the common ratio.

Given the series -10, -5, -5/2, the first term ( a = -10 ) and the common ratio ( r = \frac{-5}{-10} = \frac{1}{2} ).

Substitute these values into the formula:

[ S = \frac{-10}{1 - \frac{1}{2}} = \frac{-10}{\frac{1}{2}} = -20 ]

Therefore, the sum of the infinite geometric series -10, -5, -5/2 is -20.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.