Finding open interval of convergence

Question

Assignment:

Q1. Find the equation of the tangent line in Cartesian coordinates of the curve given in polor coordinates by 

r = 3 - 2 cos Ø, at Ø= (π / 3)

Q2.Test for convergence or divergence, absolute or conditional.  If the series converges and it is possible to find the sum, then do so.

a) ∑[∞/n=1] (3/ 2ⁿ)

b) ∑[∞/n=2] (1 / n ln n)

c) ∑[∞/n=0] (((3n²) + n +1) / (n⁴+1))

d) ∑[∞/n=1] ((n+1)/(2n+3))

e) ∑[∞/n=1] ((n!) / (2ⁿ) (n²))

f) ∑[∞/n=1] (((-1)ⁿ) /( n(^1/2)))

Q3. Find the open interval of convergence and test the endpoints for absolute and conditional convergence.

a) ∑[∞/ n=1] ((x+1)ⁿ) / ((3ⁿ)(n))

b) ∑[∞/n=1] ((x-4)⁽ⁿ⁺¹⁾) / ((n+3)²)

Provide complete and step by step solution for the question and show calculations and use formulas.