Home > #MTBoS, A Level, GCSE, Maths, Starters, Teaching > Nice summation puzzle

Nice summation puzzle

Chris Smith (@aap03102) runs a weekly maths newsletter during termtime. If you’re not on the list, I’d advise you to get on it (drop him a line in twitter). It has some great stuff in it, such as this fraction:

image

How ace is that?

He also has a puzzle of the week feature. This week’s looked cool, so I had a crack at it:

image

I thought about it a little, and saw that it boiled down to this:

image

I had the general term: 1/((n^1/2)+(n+1)^1/2) but I wasn’t sure where that would get me. I tried rationalising the denominator of the first two terms:

image

Now I could see where I was getting to, I thought I’d check the general term, to be sure:

image

Then it was a case of looking at the sum:

image

The sum of (n+1)^1/2 -n^1/2 for n=1 to n=91808

Then I cancelled:

image

Leaving just

91809^1/2 -1^1/2

Which is

303-1 =302

A lovely neat solution to a lovely summation problem which I hope to try in my sixth formers soon, and which I hope will work well with the new GCSE specifications.

Advertisements
  1. No comments yet.
  1. No trackbacks yet.

Comments welcome......

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: