7. [6/11 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 9.9.014.MI.SA. This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not b Tutorial Exercise Find a power series for the function, centered at c, and determine the interval of convergence. f(x)- 3 c=6 3x+2 Step 1 Rewrite the original function f(x) after adding and subtracting 18 in the denominator as follows. 3x+2 (x)/ 3 3x+2+18 18 20+3x-18 3 18 20+(3 )(x-6) Step 2 Divide the numerator and denominator of the function f(x) - f(x)- (x-6) 20 20+ 3 by 20 to put it in the form of a geometric series. )(x-6) Step 3 Here, f(x) has been expressed as the sum on an infinite geometric series with a . and r -3(x-6) 20 20 Therefore, the power series for the function f(x) can be written as the sum of the infinite geometric series. 3 3x + 2 (-3)(x-6) = - 20 719 (-3)" 3. (x-6) 310 Submit Skip (you cannot come back)