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This lesson explores the concept of infinite geometric series and how to find their sums. We'll discuss the conditions necessary for a sum to exist, particularly when the common ratio (r) is between -1 and 1. You will work through examples, including identifying geometric series and calculating their sums based on provided initial terms (a1) and ratios (r). Additionally, we will address the scenarios where the series diverges and does not yield a sum. Gain a solid understanding of these mathematical principles with detailed explanations and practice problems.
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Think about this… What will happen when n becomes really big? It will get closer and closer to zero.
The Sum of an Infinite Geometric Series: ONLY IF: there is no sum IF:
1. Find the sum of the geometric series. a1 = 5 < 1 r = 25
2. Find the sum of the geometric series. a1 = 1 < 1 r =
3. Find the sum of the geometric series. a1 = 1/2 > 1 r = No Sum
4. Find the sum of the geometric series. a1 = 1 < 1 r =
5. Find the sum of the geometric series. a1 = 3 < 1 r =
5. Find the sum of the geometric series. a1 = 5 > 1 r = No Sum
6. Determine if the series is arithmetic, geometric, or infinite geometric. infinite geometric arithmetic geometric