Question

How does (1/2)^n (1-2^n+1 / 1-2) = - (1/2)^n (1-2^n+1)

Answer 1

this is in my professors notes when solving a problem \[(\frac{1}{2})^n(\frac{1-2^{n+1}}{1-2})=-(\frac{1}{2})^n(1-2^{n+1})\]How in the world is this true?

Answer 2

\[\Large\bf\sf \left(\frac{1}{2}\right)^n\left(\frac{1-2^{n+1}}{\color{red}{1-2}}\right)=\left(\frac{1}{2}\right)^n\left[\color{red}{\frac{1}{-1}}\left(1-2^{n+1}\right)\right]\]

Answer 3

Do you understand where the negative in front is coming from now?

Answer 4

Just in case you're rusty on your fractions, here's an example of what I did:
\[\Large\bf\sf \frac{stuff}{a}\quad=\quad \frac{1}{a}\cdot (stuff)\]

Answer 5

I must be really rusty on my fractions cus I don't recognize that at all...do you mind showing me how this is true? Or telling me the name of the property/theorem so I can look it up?

Answer 6

wait, nvm, yes I do recognize that..

Answer 7

Oh ok :x

Answer 8

oh gosh...I see what I am doing. I've gotten so used to dealing with variables I didn't realize that 1-2 is a constant xD thanks

Answer 9

XD