Exam 9: Infinite Series

Suppose the annual spending by tourists in a resort city is $200 million. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the same city, and so on. Write the expression that gives the total amount of spending generated by the $200 million after n years.

Use the Direct Comparison Test to determine the convergence or divergence of the series

Find the sum of the convergent series by using a well-known function. Round your answer to four decimal places.

Use the Root Test to determine the convergence or divergence of the series .

Write the first five terms of the sequence.

Use the Direct Comparison Test to determine the convergence or divergence of the series .

is the series converges.

Use the Direct Comparison Test (if possible) to determine whether the series converges or diverges. ​

Find the sum of the convergent series.

State where the power series is centered.

Determine the convergence or divergence of the series .

Use a power series to approximate the value of the integral with an error of less than 0.01. Round your answer to two decimal places. ​

Find a power series for the function centered at 0.

Use the Limit Comparison Test to determine the convergence or divergence of the series .

Find the sum of the convergent series.

Find a geometric power series for the function centered at 0.

Use the definition to find the Taylor series (centered at c) for the function.

Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x. ​ ​

Find the sum of the convergent series

Consider the function given by . Find the interval of convergence for .