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2 Consider the series n 1 n 2 n 1 a x Use your computer to graph the functions f x 32 and g x 3 2 on the same set of axes You can use Desmos or your graphing calculator Set the scale on the horizontal axis so the x values go from 1 to 100 We are interested in comparing the functions for large values of x and when x is large both f x and g x are quite small Thus you should set the scale on the vertical axis to view the y values between 0 and 1 If you are using Desmos use the wrench button at the top right of your screen to set the vertical scale b Now use your computer to plot the function f x from part a together with h x You may have to experiment to find a range of y values that will enable you to see both functions on the same axes f x f x limx and limx h for the functions in parts a and b c Calculate above You can do this by hand or use the graphs of the quotients on desmos and see what happens as x goes to You don t have to show your work here but what are the limits d Look at the results of parts a through c and the statement of the LCT Should 1 you compare the series En 1 n 2 7 with n 1 7 2 or with n 1 Explain your choice after considering which term dominates the denominator for large values of n n 1n n e Does the series n 1 n 2 n converge Use the LCT and your knowledge of p series to justify your conclusion

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