use the ratio test to find the radius of convergence for (n^n*x^n)/9^n
Y yam New member Joined Jan 24, 2022 Messages 3 Jan 24, 2022 #1 use the ratio test to find the radius of convergence for (n^n*x^n)/9^n Attachments Screen Shot 2022-01-24 at 6.41.17 pm.png 156.8 KB · Views: 5
blamocur Elite Member Joined Oct 30, 2021 Messages 3,151 Jan 24, 2022 #2 Looks good so far. What about limn→∞(n+1)n+1nn\lim_{n\rightarrow\infty} \frac{(n+1)^{n+1}}{n^n}limn→∞nn(n+1)n+1 ? Hint: (n+1)n+1nn>n+1\frac{(n+1)^{n+1}}{n^n} > n+1nn(n+1)n+1>n+1
Looks good so far. What about limn→∞(n+1)n+1nn\lim_{n\rightarrow\infty} \frac{(n+1)^{n+1}}{n^n}limn→∞nn(n+1)n+1 ? Hint: (n+1)n+1nn>n+1\frac{(n+1)^{n+1}}{n^n} > n+1nn(n+1)n+1>n+1
