The discussion revolves around finding the nth term of a series involving terms of the form x^n divided by varying denominators, specifically 2 and 3 raised to different powers. Participants express challenges particularly with the denominator's structure in the series.
The discussion is ongoing, with some participants providing insights into their reasoning and attempts to derive the nth term. There is a mix of interpretations regarding the series' structure, and while some guidance has been shared, no consensus has been reached on the correct formulation.
Participants have noted difficulties with the series and have requested clarification on notation, particularly regarding the use of parentheses in mathematical expressions. There is an indication of homework constraints influencing the discussion.
It looks to me like the next term in the series will be x^6/3^3. If that's correct, then there will be two formulas for this series: one for the even degree terms and one for the odd degree terms.mario mata said:Homework Statement
find the nth term
Homework Equations
x/2+(x^2)/3+(x^3)/2^2+(x^4)/3^2+(x^5)/2^3+...
The Attempt at a Solution
the numerator clearly is x^n but i have problems with the denominator
mario mata said:thank a lot but i have the answer, it ocurred me take the fisrt two memebers and develop the serie, obtaining x^2n-1/2^n+x^2n/3^n as the nth term