CHAPTER III-FRACTIONS. 49 47. Even in respect of a geometrically progressive series, the common ratio and the first term are exactly alike (in the given series and in the chosen-off part thereof) There is (however) this difference here in respect of (the first term among) the remaining number of terms (constituting the remainder-series), viz, that the first term of the (given) seres multiplied by that self-multiplied product of the common ratio, in which (product) the frequency of occurrence of the common ratio is measured by the chosen-off number of terms, gives rise to the first term (of the remainder-series). E amphs in illustration thereof 48. Calculate what the sum of the remainder-series is in relation to that (series) of which is the common difference, the first term, and is (taken to be) the number of terms, when the chosen-off number of terms (to be removed) is (taken as) 49 In relation to a series in arithmetical progression, the first term is, the common difference is t, and the number of terms is (taken to be). When the chosen-off number of terms (to be removed) is (taken as) , give out, O you who know calculation, the sum of the remainder-series. 50 What is the value of the sunr of the remainder-series in relation to a series of which the first terų is, the commun difference is, and the number of terms is (taken to he) , when the chosen-oft number of terms is ? 51. The first term is, the common diflerence is , and the number of terms is (taken as) y, and the closen-off urber of terms is taken to be or O you, who, being the abole of lolis, are the moon shining with the moou-light of wisdom, tell me the sum of the remaining unmber of termus 52. Calculate the sum of the reaming number of terms in relation to a series of which the number of terms is 12, the common difference is mus, and the first term is 43. the chosen- off number of terms being 3, 4, 5 or 8 17. See note under 110, Chap II.
- Kala is here used in the double sense of learning and the digits or
moon
