Solution: Equation 3+q 2 = 4q can be obtained from the known common ratio Q.

The solution is q= 1 or q=3.

( 1)a[20 13]=a[20 1 1]*q^2=20 1 1*q^2

So a [2013] = 2011or a[20 13]= 18099.

(2) It is known that a [n] = 3 * 3 (n-1) = 3 n.

b[n]=( 1/ln3)^2*( 1/n- 1/(n+ 1))

t[n]=( 1/ln3)^2*(( 1- 1/2)+( 1/2- 1/3)+...+( 1/n- 1/(n+ 1)))

=( 1/ln3)^2*( 1- 1/(n+ 1))

=( 1/ln3)^2 * (n/(n+ 1))

I hope it will help you a little!