I need help proving $2-\frac{2(j+2)}{2^{j+1}}+\frac{j+1}{2^{j+1}}=2-\frac{2j+4-j-1}{2^{j+1}}$

Question

This seems simple, yet I just can't figure out how the LHS equals the RHS. Why do the terms $j$ and $1$ suddenly become negative?

$$2-\frac{2(j+2)}{2^{j+1}}+\frac{j+1}{2^{j+1}}=2-\frac{2j+4-j-1}{2^{j+1}}$$

$-a+b = -(a-b)$, so there will be minus between parts of numerator. — openspace, Oct 27 '18 at 22:11

score 2 · Accepted Answer · answered Oct 27 '18 at 22:12

2

The LHS equals the RHS actually, just note that

$$2-\frac{2(j+2)}{2^{j+1}}+\frac{j+1}{2^{j+1}}=2-\left(\frac{2(j+2)}{2^{j+1}}-\frac{j+1}{2^{j+1}}\right) = 2-\frac{2j+4-j-1}{2^{j+1}}$$

answered Oct 27 '18 at 22:12

RGS

For $j = 0$ : $2 - \frac{3}{2} = 2 - \frac{3}{2}$ – openspace Oct 27 '18 at 22:15
@openspace i know, i edited the answer in the meantime, I misread the question – RGS Oct 27 '18 at 22:16
1

Thanks, this made it much clearer! – Boris Grunwald Oct 27 '18 at 22:24

score 1 · Answer 2 · answered Oct 27 '18 at 22:21

1

$$2-\frac{2(j+2)}{2^{j+1}}+\frac{j+1}{2^{j+1}}=2-\frac{2j+4}{2^{j+1}} -\frac{-j-1}{2^{j+1}}= 2-\frac{2j+4-j-1}{2^{j+1}}$$

answered Oct 27 '18 at 22:21

2 Answers2