How do you find the sum of the infinite geometric series: a1 = -5, r = 1/6?
S = a/(1-r) = -5/(1 - 1/6) = -6
To find the sum of an infinite geometric series, you can use the formula:
S = a1 / (1 - r),
where S represents the sum of the series, a1 is the first term, and r is the common ratio.
In this case, a1 is -5 and r is 1/6.
Plugging these values into the formula, we have:
S = (-5) / (1 - 1/6).
To simplify the expression, calculate the denominator first:
1 - 1/6 = 6/6 - 1/6 = 5/6.
Now, substitute this value back into the formula:
S = (-5) / (5/6).
To divide by a fraction, we can multiply by its reciprocal:
S = (-5) * (6/5).
The negative sign and 5 in the numerator can be canceled out:
S = -6.
Therefore, the sum of the infinite geometric series with a first term of -5 and a common ratio of 1/6 is -6.