Tutorial Exercise Find the radius of convergence and interval of convergence of the series.
\sum_(n=1)^(\infty ) (x^(n+6))/(9n!)
Step 1 We will use the Ratio Test to determine the radius of convergence. We have
\lim_(n->\infty )|(a_(n+1))/(a_(n))|=\lim_(n->\infty )|((x^(n+7))/(9(n+1)!))/((x^(n+6))/(9n!))|

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Tutorial Exercise Find the radius of convergence and interval of convergence of the series.

\sum_(n=1)^(\infty ) (x^(n+6))/(9n!)

Step 1 We will use the Ratio Test to determine the radius of convergence. We have

\lim_(n->\infty )|(a_(n+1))/(a_(n))|=\lim_(n->\infty )|((x^(n+7))/(9(n+1)!))/((x^(n+6))/(9n!))|

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