We set up the ratio test as follows. 4(n + 2)x+1 lim 918 an+1 an == lim 4(n+1) 4(n+1) Step 6 Now we can simplify and evaluate the limit. |x| lim n+ 2 == |x noo n+1 1 positive number R such that the series converges if lx-a n = 0 Step 7 an+1 By the Ratio Test, the series converges when lim = x