The problem involves identifying a general term for the sequence 3, -3/2, 3/4, -3/8, which features alternating signs and denominators that are powers of two. The original poster attempts to formulate a general expression but expresses uncertainty regarding the denominator and how to incorporate the constant factor of 3.
Some participants have offered guidance on including all components of the sequence in the general term. There is an ongoing exploration of whether the proposed expression accurately reflects the sequence for various values of n, indicating a productive direction in the discussion.
Participants are considering how to account for the specific structure of the sequence, including the role of the constant 3 and the powers of two in the denominators. There is an implicit understanding of homework constraints, as the discussion revolves around deriving a general term rather than providing a complete solution.
Bashyboy said:Homework Statement
3, -3/2, 3/4, -3/8,...
Homework Equations
The Attempt at a Solution
I began to write, [itex](-1)^{n+1} \frac{3}{...}[/itex], but I began to despair once I came upon the denominator. I know that every term's, except 3, denominator can be written as a power of two, but I wasn't sure on how to account for the 3.
Bashyboy said:So, would it be [itex](-1)^{n+1} \frac{3}{2^{n-1}}[/itex]