detailed solution

Directions: Solve the following problems NEATLY, COMPLETELY, and CORRECTLY. You must submit the homework through Canvas in jpeg, png, or pdf file. 1. [3pts each] Use any method to determine whether the following sequences are convergent or divergent. Then justify your answers. 3. 7 1 2. (-1)"(vn)" 71= 1 (log2 7)" sin Il. [4pts] Determine if the series M8 is absolutely or conditionally convergent. Justify your answer. Vn2 Ill. [4pts] Determine the interval of convergence of the power series ) (x - 3)" 2" + 1 IV. [3, 2pts Consider the function defined by f(x) = log3 (2x - 1) 1. Determine the Taylor series expansion about a = 1. 2. Using the first 5 terms of the Taylor series expansion in part (a), approximate the value of f (2) up to 2-decimal place value. Compare it with the actual value of f (2). V. [4pts) Using the first 4 terms of the Maclaurin series of Arc sin(t), find an approximate value up to 3-decimal place value of the definite integral Arc sin(t) dt. t