How do you find the sum of the infinite geometric series with #a_1=-5# and #r=1/6#?

Answer 1

A geometric series of first term #a# and common ratio #r# is divergent if #|r|>=1#, and convergent if #|r|<1#, in which case the sum is given by the formula #a/(1-r)#. In the present case #r=1/6# is less than 1 in absolute value, so that the series is convergent and its sum is #-5/(1-(1/6))=-6#. See Geometric Series

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Answer 2

Charles Anctil

The sum of an infinite geometric series can be found using the formula: S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. Substituting the given values of a_1=-5 and r=1/6 into the formula, we get:

S = -5 / (1 - 1/6)

Simplifying the expression, we have:

S = -5 / (6/6 - 1/6) = -5 / (5/6) = -5 * (6/5) = -6

Therefore, the sum of the infinite geometric series with a_1=-5 and r=1/6 is -6.

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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.