Math 152 Lab 6 - ExercisesExercisesThere will be four (4) assignments for this lab. Two will be chosen from the Laboratory Project on page 723 in Stewart. Twomore will be chosen from the four assignments originally accompanying lab 6. Choose the two from the Laboratory Project in the textbook on Logistic Sequences that interest you most. In addition, choosetwo more that you would like to explore from those included with this lab below.Be sure to include in your report your reasons for your choices.ü Assignment 1: Evaluating SeriesUse Mathematica to evaluate the following series:è⁄n=1¶I‰pMnè⁄n=1¶6 n2+2 n-1nHn+1LI4 n2-1MYour answer should be the values for the two series.In[34]:=ü Assignment 2: Evaluating Partial SumsDetermine via trial and error the number of terms of the Harmonic Series ⁄n=1¶1n for which the partial sums exceed 5, 10, and 20,and comment on these values. Your answer should include:è The amounts of terms needed to exceed 5, 10, and 20.è A conjecture as to how fast the amount of terms grows with the value to exceed (e.g. logarithmically, linearly, quadratically, exponentially, etc).In[35]:=ü Assignment 3: An Alternating SeriesInvestigate the Alternating Harmonic Series⁄n=1¶H-1Lnn, and calculate a partial sum that is within 0.001 of the infinite sum. Youranswer should include:è A Point or Bar plot of the sequence H-1Lnn, which shows at least the first eight elements.è A Point or Bar plot of the sequence of partial sums ⁄i=1nH-1Lii, which show at least the first eight elements.è An estimate of the difference between the fourth partial sum and the value of the series itself, obtained from the plots above.è An explanation of how the estimate above relates to the plots above.è A calculation of a partial sum ⁄i=1NH-1Lii that is within 0.001 of the value of the series.è An explanation of how N was obtained.In[36]:=ü Assignment 4: Using the Integral TestUse the Integral Test to assist with estimating the series ⁄n=1¶ln nn2, and calculate a partial sum that is within 0.001 of the infinitesum. Your answer should include:è A Bar plot of the sequence ln nn2 which shows at least the first eight elements and a plot of the function ln xx2 on the same axes.è A statement of how the integral Ÿabln xx2„ x is related to the sum ⁄n=abln nn2, provided a and b are integers and b > a > 1.è Calculations of the partial sums ⁄n=125ln nn2 and ⁄n=150ln nn2.è Estimates of the differences between the partial sums above and the value of the series ⁄n=1¶ln nn2, obtained via integration.è A calculation a partial sum ⁄n=1Nln nn2 that is within 0.001 of the value of the series.è An explanation of how N was obtained.In[37]:=2 Math 152 Lab 6