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Shri Mahavir Jain Aradhana Kendra
www.kobatirth.org
Acharya Shri Kailassagarsuri Gyanmandir
CHAPTER III-FRACTIONS.
46
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) series multiplied by that self-multipliod 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).
Examples 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) 1.
49. In relation to a series in arithmetical progression, the first term is 1, the common difference is t, and the number of terms is (taken to be) 3. When the chosen-off number of terms (to be removed) is taken as $, give out, you who know calculation, the sum of the remainder-series.
50. What is the value of the sum of the remainder-series in relation to a series of which the first term is i, the common difference is }, and the number of terms is (taken to be) }, when the chosen-off number of terms is ty?
51. The first term is , the common difference is }, and the number of terms is (takou as) Å, and the chosen-off number of terms is taken to be or} O you, who, being the abode of kalās *, are the moon shining with the moonlight of wisdom, tell me the sum of the remaining number of terms.
52, Calculate the sum of the remaining number of terms in relation to a series of which the number of terms is 12, the common difference is minus }, and the first term is 41, the chosenoff number of terms being 3, 4, 5 or 8.
47. See note under 110, Chap. II.
Kalá is here used in the double sensc of moon'.
learning' and 'the digits of the
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