[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) › c8.s3.55 # Mathematics in Ancient and Medieval India c8.s3.55 Mathematics in Ancient and Medieval India c8.s3.55 - **Language:** English ### [c8.s3.55](https://indike.org/pramana/ins.science.bag-1979.c8.s3.55) $t\_n = (s2n. s)/((2²+2)(4²+4)...\[(2n)²+2n\]r2n) (n = 1,2,3...).$ The successive terms t₁, t₂, t₃...are, $t₁ = (s³)/(3!r²), t₂ = (s⁵)/(5!r⁴), t₃ = (s⁷)/(7!r⁶), t₄ = (s⁹)/(9!r⁸), ......$ Then according to the rule, $jīvā = (s - t₁) + (t₂ - t₃) + (t₄ - t₅) + ......$ $= s - (s³)/(3!r²) + (s⁵)/(5!r⁴) - (s⁷)/(7!r⁶) + (s⁹)/(9!r⁸) - (s¹¹)/(11!r¹⁰) + ...... (1)$ Again, $t'\_n = (s2n. r)/((2²-2)(4²-4)...\[(2n²)-2n\]r2n) (n = 1,2,3,...)$ The successive tetms t'₁, t'₂, t'₃, ... are : $t'₁ = (s²)/(2!r), t₂ = (s⁴)/(4!r³), ... t'₆ = (s¹²)/(12!r¹¹)...$ - [Previous: c8.s3.54](https://indike.org/pramana/ins.science.bag-1979.c8.s3.54) - [Next: c8.s3.56](https://indike.org/pramana/ins.science.bag-1979.c8.s3.56) - [Up: c8.s3](https://indike.org/pramana/ins.science.bag-1979.c8.s3) --- Source: [https://indike.org/pramana/ins.science.bag-1979.c8.s3.55](https://indike.org/pramana/ins.science.bag-1979.c8.s3.55) · Pramāṇa