અહીં $S_n = cn^2$ 

$S_{n-1} = c (n – 1)^2$

$t_n= S_n – S_{n-1}   = cn^2 – c (n – 1)^2  = c (2n – 1)$  

માગેલ સરવાળો

$\sum {t_n^2} \,\, = \,\,{\sum {{c^2}\,\left( {2n\, – \,1} \right)} ^2}$

$ = \,\,{c^2}\,\sum {\left( {4{n^2}\, – \,4n\, + \,1} \right)} $

$\, = \,\,{c^2}\,\left[ {4\,\sum {{n^2}\, – \,4\,\sum n \, + \,\sum 1 } } \right]$

$ = \,\,{c^2}\,\,\left[ {4\,\frac{n}{6}\,(n+1)\,(2n\, + \,1)\, – \,4\,\frac{n}{2}\,(n\, + \,1)\, + \,n} \right]$

$ = \,\,\frac{{{c^2}\,n}}{3}\,\left[ {4{n^2}\, + \,6n\, + \,2\, – \,6n\, – \,6\, + \,3} \right]$

$ = \,\,\frac{{n\,\left( {4{n^2}\, – \,1} \right)\,{c^2}}}{3}$