Contribution of Mahaviracharya in the

Author(s): R S Lal
Publisher: Z_Deshbhushanji_Maharaj_Abhinandan_Granth_012045.pdf

Page 13

Symbolically we can write, if s. = 46,71_, Sapa = (a+a) (a+d+1), etc.,
Se Sa + Sad+Sated + ... + Sa + (n-11d
= [{ (2r-19 dP + + + ad } xn--1) + a (a+10 ] x 2
In the following stanzal 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+...+n),ne,n and En.
i.e. S = 2n +22 (+1) + ne + ni .
सकपदार्धपदाहतिरवैनिहता पदोनिता व्याप्ता। सैकपदघ्ना चितिचितिचितिकृतिघनसंयुतिर्भवति ।।
Algebraically,
n (n+1)X7_..
-x (n+1)
S
=
_
2
3
which can be proved easily by substituting values
En== n (n+1) , An+n) = } En + } En
= n (n+1) (2n+1) + n (n+1)..
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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.
गच्छस्त्रिरूपसहितो गच्छचतुर्भागताडित: सैकः । सपदपदकृतिविनिघ्नो भवति हि संघातसंकलितम् ॥
Symbolically, the above formula takes the form
Unt +27° + ES. + En = [ (n+3) x 2 +1] (+n)
1. Gss 6 2. Gss 6 जन प्राच्य विद्याएं
170 171
3071 3098
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