Exp. (b)Central Idea Write the nth term of the given series and simplify it to get its lowest form. Then, apply, Sn​=ΣTn​.Given series is1t3​+1+3t3+23​+1+3+5t3+23+33​+…∞Let Tn​ be the nth term of the given series.∴Tn​ =1+3+5+…+ to n terms 13+23+33+…+n3​=n2{2n(n+1)​}2​=4(n+1)2​S9​=∑n=19​4(n+1)2​=41​[(22+32+…+102)+12−12]=41​[610(10+1)(20+1)​−1]=4384​=96