[Pramāṇa](https://indike.org/pramana/) › [Studies](https://indike.org/pramana/ins) › [Science, technology and education](https://indike.org/pramana/ins.science) › [Mathematics in Ancient and Medieval India](https://indike.org/pramana/ins.science.bag-1979) › c7.s2.44 # Mathematics in Ancient and Medieval India c7.s2.44 Mathematics in Ancient and Medieval India c7.s2.44 - **Language:** English ### [c7.s2.44](https://indike.org/pramana/ins.science.bag-1979.c7.s2.44) (b) Āryabhaṭa I³ (476 A.D.) gave the summation of the sums of n times the 1st term of n natural numbers, (n-1) times the 2nd term of n natural numbers, (n-2) times the 3rd term of natural numbers……etc. Thus if \begin{align\*} S\_1 &= n.1 \\ S\_2 &= (n-1).2 \\ S\_3 &= (n-2).3 \\ & \dots\dots\dots\dots\dots\dots \\ & \dots\dots\dots\dots\dots\dots \\ S\_{n} &= \[ n-(n-1) \].n \end{align\*} then according to Āryabhaṭa I, \begin{align\*} & S\_1 + S\*2 + \dots \dots + S\*{n} \\ = \sum\_{n=1}n S\_{n} & \\ = n.1 + (n-1).2 & + (n-2).3 + \dots\dots + \\ & \[n-(n-1)\].n \\ = 1 + (1+2) & + (1+2+3) + \dots + (1+2+\dots + n) \\ = (n(n+1)(n+2))/6 & \end{align\*} - [Previous: c7.s2.43](https://indike.org/pramana/ins.science.bag-1979.c7.s2.43) - [Next: c7.s2.45](https://indike.org/pramana/ins.science.bag-1979.c7.s2.45) - [Up: c7.s2](https://indike.org/pramana/ins.science.bag-1979.c7.s2) --- Source: [https://indike.org/pramana/ins.science.bag-1979.c7.s2.44](https://indike.org/pramana/ins.science.bag-1979.c7.s2.44) · Pramāṇa