- #1
santa
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prove the sum of this series =pi/3
[tex]1 +\frac{ 1}{5} -\frac{ 1}{7} - \frac{1}{11 }+\frac{1}{13} + \frac{1}{17} - ...[/tex]
[tex]1 +\frac{ 1}{5} -\frac{ 1}{7} - \frac{1}{11 }+\frac{1}{13} + \frac{1}{17} - ...[/tex]
Gib Z said:Cheeky CompuChip :P You know he knows the solution, he just wants to tease us :P Look at the rest of his posts to see what I mean.
Xalos said:Pi happens to be a transcendal no. meaning-you can't get its value by any algebraic method. If this a puzzle, you could get a nobel prize for the answer.
A Nobel Prize in what? Mathematics?Xalos said:If this a puzzle, you could get a nobel prize for the answer.
A series in mathematics is a sum of a sequence of terms. It can be represented as a1 + a2 + a3 + ... + an, where an denotes the terms of the sequence and n is the number of terms in the series.
The sum of a series is the result obtained when all the terms in the series are added together. It can be a finite or infinite value, depending on the terms in the series.
To prove the sum of a series, you need to use mathematical techniques such as induction, telescoping, or the ratio test. These methods involve showing that the terms of the series approach a certain value or that the series converges to a specific value.
The value of pi/3 is equal to approximately 1.0471975511965976. It is a rational number, which means it can be expressed as a ratio of two integers, but it is also an irrational number, which means it cannot be expressed as a finite decimal or fraction.
Proving the sum of this series equal to pi/3 is significant because it shows a connection between two seemingly unrelated mathematical concepts - series and pi. It also highlights the beauty and complexity of mathematics and how seemingly simple equations can have profound implications.