Geometric Sequences and Series
Consider the geometric sequence: 1, 1/2, 1/4, 1/8, 1/16, . . . What is the ratio between successive terms? Find the sum of the first two numbers in the sequence. Now find the sum of the first three numbers. Continue finding the sums in this manner. What happens to the sum of these numbers?
Consider the geometric sequence: 1, 3/2, 9/4, 27/8, 81/16, . . . What is the ratio between successive terms? Find the sums as you did above. What happens to the sum of these numbers?
Compare the sums of the two series above.
Construct your own geometric sequences. What do you predict will happen to their sums?
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