Mathematics in Ancient and Medieval India c7.s2.60

c7.s2.60

( c ) In the *Bakhshālī Ms.*¹ certain elementary cases of complex series without sum are mentioned. These series are classified into two types viz. ( i ) *yutivarga-krama* and ( ii ) *yutagaṇita-yutakrama*. Mahāvīra² ( 850 A. D. ) gave the sum of the following complex series which may be considered as one of his highest contribution in this branch : $a+(ar)+[ (ar)r ]+$ $[ (ar)r r ]+ n terms$ $=S ±(((S′)/a-n )m)/(r-1)--$ $where S=a+ar+ar²+ n terms.$