Development of Infinite Series in India

India has a long tradition of study of Mathematics. In India, all Mathematicians and mathematics were deeply respected. The development of mathematical ideas in India should be studied from the history of Indian Mathematicians and their texts. Indian Mathematicians made significant contribution in the field of mathematics and produced a large contribution in which some concepts of calculus are present. The idea of calculus in India starts with the development of decimal number system, concept of zero and infinity, irrational numbers, trigonometry, arithmetic and geometric progression, finding the value of Pi and calculating the first order and second order differences of sine values. Now our aim is to discuss the background of Indian Mathematicians in the field of calculus. The most important core concept of calculus is infinite series. Indian mathematicians developed the concept of infinite series without using the concept of set theory and functions. We discuss how the concept of infinite series is development in India.