Blog

Find the interval of convergence of

Use the Taylor polynomial of degree 2 of f(x)=ex{“version”:”1.1″,”math”:”\(f(x)=e^x\)”} centered at x=0 to approximatee0.2{“version”:”1.1″,”math”:”e^{0.2}”}

Mark the correct statement about the series ∑n=1∞(−1)nln⁡(n)n{“version”:”1.1″,”math”:”\sum_{n=1}^\infty (-1)^n \dfrac{\ln(n)}{n}”}

Determine if the following series converges or diverges. If a series converges, find its sum. ∑n=0∞(12n+14n){“version”:”1.1″,”math”:”\sum_{n=0}^\infty \left( \dfrac{1}{2^n}+\dfrac{1}{4^n}\right)”}

Determine if the following series converges or diverges. If a series converges, find its sum. ∑n=1∞(−1)n+12n3n−1{“version”:”1.1″,”math”:”\sum_{n=1}^\infty (-1)^{n+1}\dfrac{2^n}{3^{n-1}}”}

Find the Taylor series of f(x)=ln(x){“version”:”1.1″,”math”:”f(x)= ln(x)”} centered at x=1

Find the Maclaurin series of

Determine whether the following statements are TRUE (T) or FALSE (F) in general: (i) If  (ii) If    (iii)  

Determine if the following series converges or diverges. If a series converges, find its sum ∑n=1∞(1n−1n+2){“version”:”1.1″,”math”:”\sum_{n=1}^\infty \left(\dfrac{1}{n}-\dfrac{1}{n+2}\right)”}

Consider the series ∑n=1∞an{“version”:”1.1″,”math”:”\sum_{n=1}^{\infty} a_n”} where an=nsin⁡(1/n){“version”:”1.1″,”math”:”a_n=n\sin(1/n)”}. Then limn→∞an={“version”:”1.1″,”math”:”\lim_{n\to\infty} a_n=”} _______ Does the series converge or diverge? (Write either converge or diverge) _______