- #1
Null_
- 231
- 0
I attended a talk where a physicist mentioned this sequence from n=1 to infinity and apparently the answer is -1/12? Could someone explain please?
Null_ said:I attended a talk where a physicist mentioned this sequence from n=1 to infinity and apparently the answer is -1/12? Could someone explain please?
gb7nash said:If he thinks that, he needs to get his head checked.
micromass said:Well, of course the answer isn't really -1/12, rather, the answer is that the series diverges. Or maybe that the sum is infinite.
However, to some divergent series, one still can associate a number (called: the Ramanujan sum). This Ramanujan sum is not the sum of the series in the conventional sense, but rather a substitute for the conventional sum which still has a lot of useful properties.
So, in a way, it is true that 1+2+3+...=-1/12. But one should always specify that we're working with Ramanujan sums instead of conventional sums. That's all I know from this, more information on http://en.wikipedia.org/wiki/Ramanujan_summation .
The -1/12 sequence, also known as the Ramanujan summation, is a mathematical series that appears to sum to the value of -1/12 when using a particular method of summation. It is significant in physics because it has been used in various mathematical models to describe physical phenomena, such as in string theory and quantum field theory.
The -1/12 sequence is a real number, as it can be expressed as a decimal approximation (-0.083333...). However, it is also an abstract concept in the sense that it is a result of a mathematical operation and does not have a direct physical interpretation.
The -1/12 sequence can be derived through various mathematical methods, including zeta function regularization and Ramanujan summation. Its significance lies in the fact that it has been used in physical theories and calculations, and its derivation can lead to a deeper understanding of these theories.
While the -1/12 sequence has been used in physical theories, it is not typically used to solve real-world problems. Its use is primarily in theoretical and mathematical contexts, rather than practical applications.
The -1/12 sequence has been a topic of debate and controversy in the scientific community, with some arguing against its validity and others advocating for its use in certain theories and calculations. However, its use has been supported by mathematical proofs and has been used successfully in various contexts, leading to ongoing discussions and research in the scientific community.