The sum of the first n term of a series is 3-[1/3^(n-1)]. How to obtain the expression for the nth term of the series, Un?

1 Answer
Jan 11, 2018

U_n=2/3^(n-1), or, 2*3^(1-n).

Explanation:

Let, S_n denote the sum of the first n terms of the seq. {U_n}.

Then, S_n=[U_1+U_2+...+U_(n-1)]+U_n,

rArr S_n=S_(n-1)+U_n.

:. U_n=S_n-S_(n-1),

=[3-1/3^(n-1)]-[3-1/3^((n-1)-1)],

=1/3^(n-2)-1/3^(n-1),

=1/(3^n/3^2)-1/(3^n/3),

=3^2/3^n-3/3^n=(9-3)/3^n,

=(2xx3)/3^n,

rArr U_n=2/3^(n-1), or, 2*3^(1-n).