# Thread: [SOLVED] algebra in P.M.I

1. ## [SOLVED] algebra in P.M.I

I am still having trouble following the simplification of equations in the Induction examples i am studying.
The notes I have use this:

$
[\frac{1}{2}k(k+1)] + (k+1)
$

which is simplified to
$
\frac{1}{2}(k+1)[(k+1)+1]
$

but when I do the math I get
$
[\frac{1}{2}k(k+1)] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1)
$

so if anyone could explain the steps used in the former expression I would me much appreciative

2. Originally Posted by dunsta
I am still having trouble following the simplification of equations in the Induction examples i am studying.
The notes I have use this:

$
[\frac{1}{2}k(k+1)] + (k+1)
$

which is simplified to
$
\frac{1}{2}(k+1)[(k+1)+1]
$

but when I do the math I get
$
[\frac{1}{2}k(k+1)] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1) = [\frac{1}{2}k^2 + k] + (k+1)
$

so if anyone could explain the steps used in the former expression I would me much appreciative

$[\frac{1}{2}k(k+1)] + (k+1)$

Factor out (k+1)

$(k+1)(1+\frac{1}{2}k)$

You can get a 1/2 on the outside by multiplying by 1 = (1/2)(2)

$\frac{1}{2}(k+1)(2+k)$

$
\frac{1}{2}(k+1)[(k+1)+1]
$

3. I am getting there slowly, thanks. I am sorry for my ignorance.

I know what factoring is, but could you explain the first step of how to factor out
$[\frac{1}{2}k(k+1)] + (k+1)
$

in more detail please?

4. Originally Posted by dunsta
I am getting there slowly, thanks. I am sorry for my ignorance.

I know what factoring is, but could you explain the first step of how to factor out
$[\frac{1}{2}k(k+1)] + (k+1)
$

in more detail please?
Sure. We have two terms (addends) that are both divisible by (k+1).

Maybe imagine it like this

$ab + b = b(a + 1)$

where $a = \frac{1}{2}k$ and $b = k+1$.

5. Ok, got it, just needed to refresh my brain of some basic algebra!!

Thanks, I understand the expression, but I still can't see how to divide

$[\frac{1}{2}k(k+1)] + (k+1)
$

by (k+1)