A Sign-Alternating Sum Relation

Problem

The sequence $\{a_n\}$ has partial sums $S_n$ with

S_n = (-1)^na_n + \frac{1}{2^n} + n - 3 \qquad \text{for all } n \in \mathbb{N}^*,

and

(a_{n+1} - p)(a_n - p) < 0 \qquad \text{for all } n.

Find the range of possible values of the real number $p$ .

Answer

Solution

Difficulty	8/10
Topics	Recursion, sequences, Casework

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