Recent content by HypeBeast23

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    Finding Derivatives Using Taylor/Maclaurin Polynomials

    Yes, I did as such and found n = 1 to get x^6. Thus, the coefficient of x would be -(1/192), no? Apparently, the answer was wrong.
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    Finding Derivatives Using Taylor/Maclaurin Polynomials

    Homework Statement Compute the 6th derivative of f(x) = arctan((x^2)/4) at x = 0. Hint: Use the Maclaurin series for f(x). Homework Equations The maclaurin series of arctanx which is ((-1)^n)*x^(2n+1)/2n+1 The Attempt at a Solution I subbed in x^2/4 for x into the maclaurin...
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    Limit and Convergence Questions

    Homework Statement What is the limit as n approaches infinity of: (4n+2^n)/(5n+3^n) AND Does the series from 1 to infinity of (1+n)/sqrt(1+n^6) converge absolutely, conditionally or diverge? Homework Equations L'hopital's rule, convergence tests... The Attempt at a Solution...
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    Convergence of a Series with Trig Functions

    Homework Statement *The sum from n = 1 to infinity* (cos(n*pi))^2/n*pi where n is the variable. Homework Equations All forms of convergence tests (i.e. Ratio Test, Integral Test, Alternating Series test etc.) The Attempt at a Solution I am having trouble figuring out which route...