Ramanujan

Definition

Srinivasa Ramanujan was an Indian mathematician known for his contributions to mathematical analysis, number theory, infinite series, and continued fractions. His work laid foundational aspects of modern calculus and series convergence tests.

5 Must Know Facts For Your Next Test

1. Ramanujan contributed significantly to the understanding of infinite series and their convergence properties.
2. He developed many formulas involving the sum of series, which are now fundamental in advanced calculus.
3. Ramanujan's work includes the famous Ramanujan summation, which assigns finite values to divergent series.
4. His collaboration with G.H. Hardy led to numerous important results in the theory of series and sequences.
5. Ramanujan's notebooks contain hundreds of identities and equations related to infinite series that are still being studied today.

Review Questions

• What are some key contributions of Ramanujan to the study of infinite series?
• How did Ramanujan's work influence modern calculus and series convergence tests?
• What is the significance of Ramanujan summation in dealing with divergent series?

Related terms

Convergence: A property of a sequence or series whereby its terms approach a specific value as they progress to infinity.

Infinite Series: A sum of infinitely many terms, such as $a_1 + a_2 + a_3 + \ldots$, where each term is a function of its position in the sequence.

Divergence: A property where the terms of a sequence or series do not approach any finite limit as they progress to infinity.