1, the coefficient of the general term an = 1/(n * 3 n), a (n+1)/an = n/(3n+3) →1/3 (n →∞), so the convergence radius r = 650.

When x=3, the power series becomes ∑ 1/n and diverges.

When x=-3, the power series becomes ∑ 1 (- 1) n/n, and the series converges by Leibniz theorem.

So the convergence domain is [-3,3].

2、f(x)= 1/((x+ 1)(x+2))= 1/( 1+x)- 1/(2+x)= 1/( 1+x)- 1/2× 1/( 1+x/2)

1/( 1+x)=∑(- 1)^n*x^n,- 1