Does the following series converge or diverge? State which t…

Does the following series converge or diverge? State which test you use and show all work. ∑ n = 1 ∞ ( 1 e + 4 n ) n {“version”:”1.1″,”math”:”\sum\limits_{n=1}^\infty \left(\frac{1}{e} + \frac{4}{n}\right)^n”}(Show all sufficient work in steps, use the technique or method discussed in this course and include the name of test you used.)

Does the following series converge or diverge? State which t…

Does the following series converge or diverge? State which test you use and show all work. ∑ n = 1 ∞ 1 6 n 8 + n 11 {“version”:”1.1″,”math”:”\sum\limits_{n=1}^\infty \frac{1}{6n^8 + n^{11}}”}(Show all sufficient work in steps, use the technique or method discussed in this course and include the name of test you used.)

Part A (5 points) Suppose fx{“version”:”1.1″,”math”:”fx”} is…

Part A (5 points) Suppose fx{“version”:”1.1″,”math”:”fx”} is a function which has continuous derivatives. Furthermore, the following are true: f ( 0 ) = − 2 f ′ ( 0 ) = 3 f ″ ( 0 ) = 1 f ‴ ( 0 ) = − 6 {“version”:”1.1″,”math”:”\begin{align*} f(0) &= -2 \\[5pt] f'(0) &= 3 \\[5pt] f”(0) &= 1 \\[5pt] f”'(0) &= -6 \end{align*}”} Find the third-degree Maclaurin polynomial for fx{“version”:”1.1″,”math”:”fx”}. Write your answer in the first answer box. Part B (2 points) Approximate f12{“version”:”1.1″,”math”:”f12″} using the Maclaurin polynomial you found in Part A. Write your answer in the second answer box. Hint: Do your algebra using fractions instead of decimals — it will be easier. (Show all sufficient work in steps and use the technique or method discussed in this course. )