The infinite series had originated in India by the 14th c. An explicit formula for the sum of an infinite (anantya) geometric series is given by the 15th-16th c. Nilkantha in his Aryabhatyabhasya.(Sastri 1970, commentary on Ganita 17, p. 142.)
एवं यासतुल्यच्छेदपरभागपरम्पराया अनन्ताया अपि संयोग
तस्यानंतानांपि कल्प्यामान्स्य योगस्याद्यावयविनः
परंपरांशच्छेदादेकोनच्छेदांशसामयं सर्वत्रापी समानमेव ।
which may be translated:(cf. Sarma 1972, p. 17)
The sum of an infinite [anantya] series, whose later terms (after the first) are got by dividing the preceding one by the same divisor everywhere, is equal to the first term multiplied by the common divisor, and divided by one less than the common divisor.
That is a+a + a +···= ad/d-1 .(It is assumed that the divisor d>1, so
that the common ratio is less than 1.)