Power Series

(Finney, AP Calculus BC)

Write an expression for aₙ.
Determine whether the series converges by finding the limit of partial sums.
Let Sₙ = (n+1)/(2n+5) be the nth partial sum of the series Σaₙ. Write a rule for aₙ.
Tell whether the infinite series converges or diverges.
Find the interval of convergence and the function of x represented by the geometric series.
Use differentiation to find a power series for f(x) = 2/(1−x)³
Find a power series that represents 1/x on (0,2). Hence find a power series for lnx centered at x=1.
Given Σ5xⁿ = q, solve for x in terms of q.
What conclusion can be reached by using the nth term test for divergence given the series