Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 238

CHAPTER INFRACTIONS.
20. Give the oube roots of 185 and 42.
21. O friend of prominent intelligence, give the cube roots of the cubed quantities found in the examples on) the onbing of fractions and (give also the cube root) of 242.
Thus end the squaring, square-root, cubing and cube-root of fractions.
Summation of fractional series in progression.
In regard to the summation of fractional series, the rule of work is as follows:
22. The optional number of terms (making up the fractional series in arithmetical progression) is multiplied by the common difference, and then it) is combined with twice the first term and diminished by the common difference. And when this (resulting quantity) is multiplied by the balf of the number of terms, it gives rise to the sum in relation to a fractional series (in arithmetical progression)
Examples in illustration thereof.
• 23. Tell me what the sum is (in relation to a series) of which , } and are the first term, the common difference and the number of terms (in order); as also in relation to another of which }, { and f (constitute these elements).
24. The first term, the common difference and the pumber of terms are }, } and in order in relation to a given series in arithmetical progression). The numerators and denominators of all (these fractional quantities) are (successively) increased by 2 and 3 (respectively) until seven (series are so made up). What is the sum of each of these) ?
22 Algebraically S=(nb + 2a-6)
. Cf. note under 62, Chap. JI.
23. Whenever the number of terms in a series is given as a fraction, as here, it is evident that such a series cannot generally be formed actually number of terms. But the intention seenis to be to show that the rule holds good even in such cases.