Question Number 102652 by Dwaipayan Shikari last updated on 10/Jul/20

2+18+156+1388+...n terms

Commented byDwaipayan Shikari last updated on 10/Jul/20

T_n =n.7^(n−1) +n^2   ΣT_n =((7^n .(6n−1)+1+6n(n+1)(2n+1))/(36))  is it???????

Commented byprakash jain last updated on 10/Jul/20

You cannot really deduce any  expression given only a finite  number of term.  Suppose only 4 terms are given  f(n)=a_0 +a_1 n+a_2 n^2 +a_3 n^3   and solving for given value will  give you one solution.  If f(n) satifies first 4 terms then  g(n)=f(n)+(n−1)(n−2)(n−3)(n−4)h(n)  will also satisfy the given  condition. where h(n) is any  arbitrary function of n.  T_n =n7^(n−1) +n^2 +              (n−1)(n−2)(n−3)(n−4)h(n)  is also valid. where h(n) could  be anything.