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a curious mathematical result that appears to contradict common sense
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The Ramanujan paradox isn't quite a paradox in the traditional sense. It refers to the idea that Srinivasa Ramanujan, a brilliant Indian mathematician, devised a method for assigning a value to infinite series that normally don't converge (their sum keeps growing without ever reaching a specific answer).
Here's the catch: The most famous example, the sum of all natural numbers (1 + 2 + 3 + ...), doesn't actually equal -1/12 using Ramanujan summation. It's a common misconception, and while the technique is valid in specific contexts, it doesn't apply to adding natural numbers infinitely.
Step-by-step explanation:
Normal Summation: When we add numbers, we expect a finite answer. 1 + 2 + 3 = 6. But what about 1 + 2 + 3 + ... infinitely? In this case, the sum keeps growing forever, making it divergent.
Ramanujan Summation: This is a method for assigning a special kind of value to divergent series. It's not a traditional sum, but rather a way to extract useful information from these infinite sequences.
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