A History of the Kerala School of Hindu Astronomy (in Perspective) c8.s4.24

c8.s4.24

The credit for enunciating in India, for the first time, a formula for the sum of an infinite convergent geometrical progression, goes to Nīlakaṇṭha Somayājī (born 1444). This he gives in his *Āryabhaṭīya-Bhāṣya*, while explaining the process of deriving the arc of a circle in terms of the chord by means of a computation which involves the summing up of an infinite convergent G.P. series : *evam yas tulyaccheda-paramebhaga-paramparayā anantāya api saṃyogaḥ, tasya anantānām api kalpyamānasya yogasya adyāvayavinaḥ paraspar-aṃsacchedād ekacchedāṃśasādhyam sarvatrāpi samānam eva.* (Bhāṣya on *Āryabhaṭīya*, Gaṇita. 17, edn., Trivandrum, 1930, p. 106). ‘Thus the sum of an infinite series, whose later terms (after the first) are got by diminishing the preceding one by the same divisor, is always equal to the first term divided by one less than the common mutual divisor.’