________________
Symbolically we can write, if Sa =
S Sa+Sa+sa+2+
= [{(2n)
(2n-1) d2 6
i.e. S = En + (n+1)+ n2 + n3 .
2
Algebraically,
In the following stanza a rule has been given for finding of the sum of the series which can be written symbolically in the form
1+(1+2)+(1+2+3)++(1+2+3+...+), n2, and En.
S=
a (a+1) 2
+ Sa + (n-1) d
d
+ 12/12 +ad} x(n-1)+ a (a+1)] x
n (n+1) x 7
2
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संकपदार्थपदातिरनिहता पदोनिता व्याप्या संपदा चितिचितिथितिकृतिधनसंयुतिर्भवति ॥
3
1. GSS 2. GSS
जैन प्राच्य विद्याएं
which can be proved easily by substituting values
n (n+1) 1 Σn ==
2
2
6
6
-n
X (n+1)
(n2+n)
// 202 +
Symbolically, the above formula takes the form
Sa+d
170
171
n (n+1) (2n+1)
12
+ 1/2 En
Lastly, in the following stanza a rule has been given for finding out a single formula for the sum of the four above mentioned series.
(a+d) (a+d+1) 2.
+
En2+En+ ΣSn + En = [ (n+3) × 2 + 1 ] (n2+n)
307
309
refererefight
againafen: dc: | पदपदकृतिविनिष्तो भवति हि संघात संकलितम् ॥
n(n+1)
4
etc...
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