Blog Option 4
Explain how you determine if a sum can be evaluated or not.
In order to determine if a sum for an infinite geometric series can be evaluated or not, one must first determine the ratio for the geometric sequence (in this case, 2). Then, one must make sure the absolute value of the ratio is greater than or smaller than 1. If the absolute value of the ratio is smaller than 1, the series is considered to be convergent and the sum of the infinite series CAN be evaluated; if the absolute value of the ratio is greater than 1, which is the case for the example above, the series is considered to be divergent and the sum of the infinite series CANNOT be evaluated.
What formula do you use to evaluate an infinite geometric sum and explain how to do a correct substitution.
*Formula obtained from IB Mathematics SL formula booklet
In order to use the formula above, make sure the infinite geometric series fulfils the requirement to the right, and simply replace u with the subscript 1 with the value for the first term and r with the ratio for the geometric series. Finally, solve the equation to find the sum of the infinite geometric series.