Infinite Geometric Series
Students will be able to find the sums of infinite geometric series with ratios having an absolute value of less than one. Learn how to determine whether an infinite geometric series has a sum based on the common ratio criterion. Explore examples to calculate the sum of infinite geometric series and how to express infinite repeating decimals as fractions.
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Presentation Transcript
11.6 INFINITE GEOMETRIC SERIES STUDENTS WILL BE ABLE TO FIND THE SUMS OF INFINITE GEOMETRIC SERIES HAVE RATIOS WITH AN ABSOLUTE VALUE OF LESS THAN ONE
SUMS INFINITE GEOMETRIC SERIES SOME GEOMETRIC SERIES HAVE A SUM AND SOME DO NOT FOR AN INFINITE GEOMETRIC SERIES TO HAVE A SUM, THE COMMON RATIO MUST BE BETWEEN -1 AND 1 THE SUM OF AN INFINITE GEOMETRIC SERIES WITH COMMON RATIO -1<R<1 IS: t = S 1 1 r
EXAMPLE 1 FIND THE SUM OF THE INFINITE GEOMETRIC SERIES. IF THE SERIES HAS NO SUM, SAY SO. 8-4+2-1+
EXAMPLE 2 FIND THE SUM OF THE INFINITE GEOMETRIC SERIES. IF THE SERIES HAS NO SUM, SAY SO. 8+12+18+27+
INFINITE REPEATING DECIMALS INFINITE REPEATING DECIMALS CAN BE EXPRESSED AS AN INFINITE GEOMETRIC SERIES THE SUM THEN CAN BE CALCULATED AND EXPRESSED AS A FRACTION
EXAMPLE 3 WRITE 0.121212121212 AS A COMMON FRACTION.
