Question

if converges, then converges to what?
did I do this one correctly?

Answer 1

So my series was
\(\large \displaystyle x+2x^2+x^3+2x^4+x^5+2x^6+x^7+2x^8 \)

Answer 2

Now, what it converges to is the question I will answer.

Answer 3

The common ratio is x^2, and the terms are as follows
a(1)=x+2x^2
a(2)=x^3+2x^4
a(3)=x^5+2x^6
and so forth

Answer 4

the series will converge to \(\LARGE\frac{x+2x^2}{1-x^2}\) if it is convergent

Answer 5

and it is convergent when
|x^2|<1
x^2<1
-1<x<1

Answer 6

it is right !!

Answer 7

tnx