Thread: Factoring

Hi all,

I am looking at mathamatical induction and seem to be stuck on why the answer to a factoring step is correct.

r(r+1)+2(r+1) factored by r+1 gives (r+1)(r+2)

2(r+1) factored by r+1 to give (r+2) is clear but I cannot fathom r(r+1) factored by r+1 gives r+1.

Here is the link to the page on induction and is below line 1
Mathematical induction - Topics in precalculus

This is my first post here so please be gentle.

Originally Posted by ilj

2(r+1) factored by r+1 to give (r+2) is clear

can you elaborate this?

Ok,

2(r+1) simplified gives 2r+2

2r+2/r+1=r+2

Hmm that doesn't look correct.

Am I on the wrong track completly?

This is the progression I am stuck on.

1+2+3+....+k+(k+1) = k(k+1)/2 +(k+1)

=k(k+1)+2(k+1)/2

on adding these fractions

=(k+1)(k+2)/2

for easiness, take (k+1) as 'a'

then [k(k+1)+2(k+1)]/2 will be [ka+2a]/2

since a is common, [ka+2a]/2=a[k+2]/2 which is (k+1)(k+2)/2

That is a very good explanation, thank you very much, I will use that method again.

Are you asking why r(r + 1) + 2(r + 1) = (r + 1)(r + 2)? If so, it should be obvious that there is a common factor of (r + 1)...

Yes I did know that but didn't know how to use factoring, that was my issue. After 30 or so years you tend to forget a few things.