1. ## Series problem (again!)

Hi guys, so i was doing this one question and cant find a way through. It goes by like this :
What is the condition such that the series

1+[7/(3x+5)]+[7+(3x+5)^2].... is converge
hence show that the sum of the above series is 3x-5/3x-12

2. ## Re: Series problem (again!)

Originally Posted by nisbahmumtaz
1+[7/(3x+5)]+[7+(3x+5)^2].... is converge
hence show that the sum of the above series is 3x-5/3x-12
Could you write the series and the answer correctly? I suspect the answer is not $\displaystyle 3x-\frac{5}{3x}-12$.

4. ## Re: Series problem (again!)

Originally Posted by nisbahmumtaz
Hi guys, so i was doing this one question and cant find a way through. It goes by like this :
What is the condition such that the series
1+[7/(3x+5)]+[7+(3x+5)^2].... is converge
hence show that the sum of the above series is 3x-5/3x-12
Is that + correct? Could it be $\displaystyle \frac{7}{(3x+5)}+\frac{7}{(3x+5)^2}+\frac{7}{(3x+5 )^3}\cdots~?$
If not then it diverges.

5. ## Re: Series problem (again!)

And $\displaystyle 1+\sum_{i=1}^\infty\frac{7}{(3x+5)^i}=\frac{3x+11} {3x+4}$ (using geometric progression).

Edit: added ^i to the formula.

6. ## Re: Series problem (again!)

Originally Posted by Plato
Is that + correct? Could it be $\displaystyle \frac{7}{(3x+5)}+\frac{7}{(3x+5)^2}+\frac{7}{(3x+5 )^3}\cdots~?$
If not then it diverges.
Yikes. Darn it this iphone keyboard. Its supposed to be " / " not "+"

7. ## Re: Series problem (again!)

Originally Posted by nisbahmumtaz
Yikes. Darn it this iphone keyboard. Its supposed to be " / " not "+"