Find the radius of convergence, r, of the series. ∞ xn 2n − 1 n = 1 r = 1 find the interval, i, of convergence of the series. (enter your answer using interval notation.) i =

Assuming the series is



The series will converge if



We have



So the series will certainly converge if , but we also need to check the endpoints of the interval.

If , then the series is a scaled harmonic series, which we know diverges.

On the other hand, if , by the alternating series test we can show that the series converges, since



and is strictly decreasing.

So, the interval of convergence for the series is .

I’m not absolutely sure but i think it’s 7x6x5x4x3x2=5040 because as the first character you can take any of the 7 given then you are left with 5 then 6 then 4 etc.