Power Series

Question

Power Series

anonymous · Answer

attachment

anonymous · Answer

Given f(x) Find...

anonymous · Answer

My trouble is, what happen to the "-1". I have tried working it out and i don't know how they got rid of it?

anonymous · Answer

take the absolute value, that's how they get rid of it

anonymous · Answer

they replaces each $x$ by $2x$
they divide every term by $x$
then they changed the sign of every term

anonymous · Answer

@satellite73 yes but what happen to the "-1" ? :|

anonymous · Answer

oh i am an idiot
they subtracted 1!

anonymous · Answer

that isn't "times $-1$ that is just -1

anonymous · Answer

@satellite73 ohhh so its just ONE "-1" and that is why the "1" at the beginning went away?

anonymous · Answer

$$1-\frac{x}{8}+\text{blah blah blah}-1=\frac{x}{8}+\text{blah blah blah}$$

anonymous · Answer

yes, that advanced arithmetic where $1-1=0$ lol
i fell for it too...

anonymous · Answer

@satellite73 ah! i get it. what i was doing was putting "-1" after ever "2x" i substituted

anonymous · Answer

So it left me with a lot of "-1" 's

anonymous · Answer

good!

anonymous · Answer

oops

anonymous · Answer

actually this is a good problem for that reason
like asking if 
$$\sum_{n=0}^{\infty}\frac{1}{2^n}=2$$ then what is 
$$\sum_{n=1}^{\infty}\frac{1}{n^n}$$

anonymous · Answer

typo but you get the idea
arithmetic still works in power series
so does multiplication, division etc