Ganitasara Sangraha of Mahavira

SR No.: 011112
Original Sutra Author: N/A
Author: Rangacharya
Publisher: Rangacharya
Publication Year: 1912
Total Pages: 531
Language: English
Classification: Book_English
File Size: 24 MB

Page 250

48
GANITASA LA SANGRAHA.
Examples in illustration thereof. 44. The number of terms are 5, 4 and 3 (respeotively) and the common ratios as well as the equal) common differences are 4, and (in order). What is the value of the corresponding) first terms in relation to these (sets of two series, one in geometrical progression and the other in arithmetical progression), which are characterised by sums of the same value
Thus ends the summation of fractions in series.
Vyutkalita of fractions in series.
The rule for performing the operation of vyutkalita is as follows:
45. (Take) the chosen-off number of terms as combined with the total number of ternis (in the series), and (take) also your chosen-off number of terms (separately). Multiply each of these quantities by the common difference and diminish (the products) by the common difference; (then) multiply by tiro; and these (resulting quantities), whon multiplied by the half of the remaining number of terms and by the balf of the chosen-off number of terms (respectively), give rise to the sum of the remainder-sories and to the sum of the chosen-off part of the (given) serios (in order).
The rule for finding ont the first term in relation to the remaining number of terms (making up the remainder-series) :
46. The first term (of the series), diminished by the half of the ooinmon differenog, and combinerl with the chosen-off number of terms as multiplied by the common difference, as also with the balf of the common difference, (gives) the first term of the remaining number of terms (making up the remainder-series). And the common difference (of the remainder-series) is the same as what is found in the given series.
45. Cf. note ander 106, Chap. II. 48. Cf. noto under 109 Chap. II.