The sum of the first 10-terms of the series 51.2.3+72.3.9+93.4.27+… is

Tn=nth term of the series n(n+1)⋅3n=2n+3n(n+1)3nLet⁡2n+3n(n+1)3n=3n−1n+113n=1n3n-1−13n(n+1)Sn=∑Tn=∑1n3n-1−13n(n+1) =1−12.3+12.3−13.32+..+1n⋅3n−1−1(n+1)3n=1−1(n+1)3nS10=1−111.310