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Contribution of Mahaviracharya in the development of theory of Series
Dr. R. S. LAL
In the present paper, an attempt has been made to summarize some of the salient features of the work of the great ancient Indian Mathematician Mahaviracharya (850 A.D.) on the development of theory of series as evinced from his renowned mathematical text Ganita Sarasangraha. No doubt his predecessors Aryabhata I (476 A.D.) and Brahmagupta (599 A.D.) had their contributions to the subject, yet Mahaviracharya can be named as the first amongst them who put the subject elaborately using lucid methods and charming language.
The text GSS consists of nine chapters but it is only chapters II, III and VI which contain the sutras regarding series. In chapters II the A.P. and GP. are given in detail. For example, the following sutra gives the sum of the A.P. whose first term, common difference and number of terms are known.
रूपेणोनो गच्छो दलीकृत: प्रचयताडितो मिश्रः ।
प्रभवेण पदाभ्यस्तः सङ्कलितं भवति सर्वेषाम् ।। Algebraically if a=first term, d=common difference and n=number of terms and s=the sum of the series then
s = [(n-1)d+2.]
The above formula has been given in three ways29394. In the following sutra ille method is given to find out the number of terms of the series if the first term, common difference and the sum of the series be known.5
अष्टोत्तरगणराद्विगुणादयुत्त रविशेषकतिमहितात् ।
मूलं चययुतमधितमायूनं चयहृतं गच्छः ॥ Symbolically, if a=first term, d=common difference, S=sum of the series and n=number of terms then
n= V(2a—d)2+8d?s –2a+d
2d2
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Note :-For references : See Ganita Sarasangraha by Sh. L. C. Jain Ch.
Sloka GSS GSS
62 3. GSS 2 4. GSS 3. GSS
अन प्राच्य विद्याएँ
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