Checkpoint 6 Answer

`|b_(k+1)//b_k|=|x|^2(2k+1text[)/(]2k+3) rarr |x|^2 text(as ) k rarr oo`. This limit will be less than `1` for `text[|] x text[|] <1`. Thus the series converges for `-1<x<1` and diverges for `x>1` and `x<-1.` The test doesn't tell us anything about what happens when `x=1` or `x=-1`. (However, we know from the Alternating Series Test that the series converges at both endpoints. The sums are `pi//4` and `-pi//4`, respectively.)