Find the Nth Term: Simplifying the Denominator

[mario mata]

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]

i have many problems with this serie because of the denominator

 

[Mark44]

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

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]

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

 

[Mark44]

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

I can't even guess what you mean by this: x^2n-1/2^n+x^2n/3^n

Please use parentheses around the exponents and numerators and denominators of fractions.