[SOLVED] algebra in P.M.I

**dunsta** · June 8th 2010, 09:22 PM

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

**undefined** · June 8th 2010, 10:10 PM

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] $

**dunsta** · June 8th 2010, 10:35 PM

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?

**undefined** · June 8th 2010, 10:40 PM

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 $b = k+1$ .

**dunsta** · June 9th 2010, 05:18 AM

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)

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