I have a question and am unsure how to start it:

Prove by induction that

(sum from k=1 to n)of

k(k+1)...(k+a) = 1/(a+2)*n(n+1)(n+2)....(n+a+1)

Printable View

- Dec 10th 2008, 04:48 AMpoppy12345PROVE BY INDUCTION
I have a question and am unsure how to start it:

Prove by induction that

(sum from k=1 to n)of

**k(k+1)...(k+a) = 1/(a+2)*n(n+1)(n+2)....(n+a+1)** - Dec 10th 2008, 07:19 AMGrandadProof by induction
Hello -

Tricky to know where to start, isn't it? Is it that we vary, or ?

Well, start in the usual way, by writing a proposition about , and let take care of itself. So:

Let

Then the propositional function is defined as:

Then write down the sum as the term you get when .

You'll find you can then take out lots of common factors, and eventually express this as , thus showing that .

Finally, you'll need to prove that is true for any .

I hope I've given you enough to go on. Let me know if you need more help.

Grandad - Dec 10th 2008, 07:43 AMjames_bond
Suppose . So we need to show that .

by the assumption. So this should be equal to : QED - Dec 10th 2008, 07:51 AMmitch_nufclol
DR Duncans class by any chance? ;)

- Dec 11th 2008, 01:19 AMpoppy12345
yea

- Dec 11th 2008, 06:19 AMmitch_nufc
are you still stuck on that or anything? i handed in today, pretty confident everythings right :)

- Dec 11th 2008, 07:17 AMpoppy12345
well i think ive managed but going tomorro. never very confident but neva mind!

- Dec 11th 2008, 07:43 AMmitch_nufc
im always happy to help if ya stuck... just shout, whats ur name?