Step 5 Now we must find the radius of convergence for the Maclaurin series 4(n + 1)x". That is, the positive number R such that the series converges if (x - al R. We can use the ratio test to find R. First, we set up the ratio test as follows. 3=0 lim 318 an =lim 818 4(n + 2)x + 1 4 n+1 4(n+1) Step 6 Now we can simplify and evaluate the limit. [x] lim 918 n+2 n+1 = |x| 1 Step 7 1) By the Ratio Test, the series converges when lim Submit Skip (you cannot come back) 318 1 = x < 1. Therefore, the radius of convergence is R = an x