Help with calc. problem?

Question

find a power series representing 1/(1+x^6) and specify its radius of convergence

Answer 1

this is the sum of a geometric series with r=-x^6

1-x^6+x^12 -x^18++++
The radio of covergence of a geometric series is I r I <1
so I xI <1

Answer 2

Remeber S = a/(1-r) for geometric series when IrI< 1
so a = 1 and r = x^6 Ix^6I<1
1 + x^6 + x^12 + x^18 + ...
Series notation
Sum from {n=0 to infinity} of x^(6n)

radius of convergence is 1
strictly between -1
:)