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From: =?UTF-8?q?Fabiana=20=F0=9F=9A=80=20=20Campanari?=
<113218619+FabianaCampanari@users.noreply.github.com>
Date: Sun, 19 Jan 2025 23:55:00 -0300
Subject: [PATCH] Update README.md
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Signed-off-by: Fabiana π Campanari <113218619+FabianaCampanari@users.noreply.github.com>
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README.md | 23 +++++++++++++++++------
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@@ -201,19 +201,30 @@ Joseph Fourierβs development of Fourier analysis allowed quantum mechanics to
### 4. **Srinivasa Ramanujan (1910β1920)**
ββββββββββββββ
- * Srinivasa Ramanujan made groundbreaking contributions to mathematics, particularly in the realms of modular forms and infinite series. His work has had a lasting impact on various fields, including quantum gravity and string theory.
+ * Srinivasa Ramanujan made groundbreaking contributions to mathematics, particularly in the realms of modular forms and infinite series. His work has had a lasting impact on various fields, including quantum gravity and string theory.
- ### ***Ramanujan's Infinite Series for $\huge \color{DeepSkyBlue} $( \pi \)$ :***
+**Srinivasa Ramanujan (1910β1920)**
- One of his most famous formulas is an infinite series for $\large \color{DeepSkyBlue} \frac{1}{\pi}$ :
+Srinivasa Ramanujan made groundbreaking contributions to mathematics, particularly in the realms of modular forms and infinite series. His work has had a lasting impact on various fields, including quantum gravity and string theory.
- $\huge \color{DeepSkyBlue} \frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum_{n=0}^{\infty} \frac{(4n)!(1103 + 26390n)}{(n!)^4 396^{4n}}$
+ ### **Ramanujan's Infinite Series for \( \pi \):**
-
+One of his most famous formulas is an infinite series for \( \frac{1}{\pi} \):
-
+\[
+\frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum_{n=0}^{\infty} \frac{(4n)!(1103 + 26390n)}{(n!)^4 396^{4n}}
+\]
+
+Where:
+
+- **\( n \)**: Summation index.
+This series converges extraordinarily rapidly, making it highly efficient for calculating \( \pi \) to many decimal places. In 1985, William Gosper used this formula to compute \( \pi \) to 17 million digits.
+Ramanujan's deep insights into infinite series and modular forms continue to influence modern mathematical research and applications.
+
+
+