2) Find the interval of convergence if
The interval of convergence is
Step 1 :Rewrite the series as
Step 2 :Apply the Ratio Test:
Step 3 :Simplify the expression:
Step 4 :Take the limit as n approaches infinity:
Step 5 :For the series to converge, the result of the Ratio Test must be less than 1:
Step 6 :Solve the inequality:
Step 7 :Multiply all sides by 4:
Step 8 :Distribute the 3:
Step 9 :Add 3 to all sides:
Step 10 :Divide all sides by 3:
Step 11 :The interval of convergence is