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) _______

Find the limit of the sequence limn→∞n5n{“version”:”1.1″,”math”:”\lim_{n\to\infty} \sqrt{\dfrac{n}{5}}”}

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

Solve 32x−1=2x+1{“version”:”1.1″,”math”:” 3^{2x-1}=2^{x+1} “}

Calculate log2⁡0.5{“version”:”1.1″,”math”:”\log_2{0.5}”}

Sketch the graph of the function and find its range f(x)=5+3−x{“version”:”1.1″,”math”:”f(x)=5+3^{-x}”}

Let f(x)=x{“version”:”1.1″,”math”:”\(f(x)=\sqrt{x}\)”}. Write the functions resulting from the following transformations.(a) f1(x)={“version”:”1.1″,”math”:”\(f_1(x)=\)”} shift the graph of f(x){“version”:”1.1″,”math”:”\(f(x)\)”} two units to the left.(b) f2(x)={“version”:”1.1″,”math”:”\(f_2(x)=\)”} reflect the graph of f1(x){“version”:”1.1″,”math”:”\(f_1(x)\)”} about the x-axis.(c) f3(x)={“version”:”1.1″,”math”:”\(f_3(x)=\)”} shift the graph of f2(x){“version”:”1.1″,”math”:”\(f_2(x)\)”} three units down and then reflect about the y-axis.