Below are six methods for determining whether an infinite series coverges or diverges. A. Integral Test B. Direct and Limit Comparison Tests C. Alternating Series Test D. Ratio Test E. Root Test F. Divergence Test From the above six methods, specify the best method to test the convergence or divergence of the following series as well as the reason for your choice. You need not complete the test. \sum_{n=1}^{\infty} \frac{1}{n+n \cos ^{2} n} \sum_{k=1}^{\infty} \frac{2^{k} k !}{(k+2) !} \sum_{k=1}^{\infty} \frac{5^{k}}{3^{k}+4^{k}} \sum_{1}^{\infty}(-1)^{n-1} \frac{n-1}{n^{2}+n}

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9

Fig: 10

Fig: 11

Fig: 12