Question 2(20 points): a) In how many different ways you can show that the following series is convergent or divergent? Explain in detail. ∑_(n=1)^[infinity]▒n^5/7^n .
b) Can you find a number A so that the following series is a divergent one. Explain in detail. ∑_(n=3)^[infinity]▒3^An/n^n .
Question 3 (20 points): a) Which tests can be used to check the convergence or divergence of the following series? Explain in detail. ∑_(n=1)^[infinity]▒3/(n^2+9).
b) Which tests can be used to check the convergence or divergence of the following series? Explain in detail.
∑_(n=1)^[infinity]▒〖(-1〗 )^n n^6/3^n .