"गणितसारसंग्रह": अवतरणों में अंतर
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अनुनाद सिंह (वार्ता | योगदान) |
अनुनाद सिंह (वार्ता | योगदान) |
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पंक्ति 59:
In the ''Gaṇita-sāra-saṅgraha'' (GSS), the second section of the chapter on arithmetic is named ''kalā-savarṇa-vyavahāra'' (lit. "the operation of the reduction of fractions"). In this, the ''bhāgajāti'' section (verses 55–98) gives rules for the following:<ref name=k497/>
* To express 1 as the sum of ''n'' unit fractions (
{{quote|रूपांशकराशीनां रूपाद्यास्त्रिगुणिता हराः क्रमशः ।<br>
द्विद्वित्र्यंशाभ्यस्ताव आदिमचरमौ फले रूपे ॥}}
{{quote|When the result is one, the denominators of the quantities having one as numerators are [the numbers] beginning with one and multiplied by three, in order. The first and the last are multiplied by two and two-thirds [respectively].}}
:: <math> 1 = \frac1{1 \cdot 2} + \frac1{3} + \frac1{3^2} + \dots + \frac1{3^{n-2}} + \frac1{\frac23 \cdot 3^{n-1}} </math>
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