Example of sum to infinity
Example of sum to infinity
IB Year 5 | Grade 11
The second term of a geometric progression is \(24\), and the fifth term is \(\frac{8}{9}\).
Calculate the first term, the common ratio and the sum to infinity, if it exists.
A second series is formed by squaring each term of the given geometric progression. Find the sum to infinity of this second series, justifying its convergence.
Solution:
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Answer:First term \(72\), common ratio \(\dfrac13\), sum to infinity \(108\). Squared-term series converges with sum \(5832\).
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