Consider the power series P(x)= _ n=1 ^ (-3)^ ,n-1 (x+2)^ n n ,5^ n
MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Consider the power series
P(x)=n=1∑∞n5n(−3)n−1(x+2)n.
Answer the questions below.
(a) Derive a closed-form expression for P(x) in terms of elementary functions. Show all algebraic steps that lead from the series to the function.
(b) Determine the radius of convergence of P. Clearly indicate any tests you apply as part of your work.
(c) Find the complete interval of convergence, including a justification for convergence or divergence at each endpoint.