________________
No. II]
MATHEMATICS OF NEMICANDRA.
To find the number of terms of a series in A.P. whose first and last terms are known as well as the common difference, Nemicandra gives the formula,1
l-a
b.
Geomteric Progression. To find sum of a series in geometric progression (guna-dhāra), Nemicandra describes the following rule:
n=
"Multiply mutually as many common ratios as there are number of terms in the series; the product is diminished by unity and then divided by the common ratio minus one and multiplied by the first term: the result is the sum of the series in geometric progression,"
2
Algebraically
1 Ibid, Gatha 57.
where a the first term of a series in G. P., the common ratio and S the sum.
Examples from Nemicandra :3
(1+22+23+...+2") a
A= 10 +10% +108
p p
=
Sa
s=a (1),
=
+1
=
= (1-1),
9
=
p
9
p
80
+
(a little less than);
p 800
p
p + 8.10 8.102
p
+... + 10"
+....
=
+ +
...
(2n+1-3) a;
p
=
- 12/24 (-11),
72
10n
72(a little less than).
2 Trilokasara, Gāthā 231.
33
p 8.10
9
3 Ibid, Gathas, 796-7.
