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)
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