\prod_{j=1}^{k+1}_{j} - 1 = \prod_{j=1}^{k+1}_{j} - 1 + (k+1) \prod_{j=1}^{k+1}_{j}
Ok so I also cancel out the -1 on both sides, then I factor out
\prod_{j=1}^{k+1}_{j} and I get
\prod_{j=1}^{k+1}_{j} = 1 +(k+1)(\prod_{j=1}^{k+1}_{j})
then cancel out the...
Ok so first I replaced all the sum stuff with the right hand side to make it easier to read. By substituting the right side of left side of the initial equality with the right side. That should work fine right?
The I have:
\prod_{j=1}^{k+1}_{j} - 1 = \prod_{j=1}^{k+1}_{j} - 1 +...
Homework Statement
\sum_{i=1}^{n} (i \prod_{j=1}^{i}_{j}) = \prod_{i=1}^{n+1}_{i} - 1
Homework Equations
The Attempt at a Solution
First show the base case. That easys just shows it holds for n=1. Not sure where to go from there? What term do I add to both sides? Not really sure what...
Homework Statement
Prove by induction, that for all integer n where n>= 1
\sum_{i=1}^{n} i(i+1)(i+2) = \frac{n(n+1)(n+2)(n+3)}{4}
Homework Equations
The Attempt at a Solution
First question is do I start at i=0 or i=1? It says >=, so not sure.
Ok then I added...
Can you explain what you did?
Ok I'm still a bit confused
To show its true for n=2 I do
1/1^2+ 1/2^2 <(2 - 1/1) + (2- 1/2)
Is that how you prove it for n=2?
Homework Statement
Prove by induction that for an integer n where n>1 , http://img3.imageshack.us/img3/5642/prob1q.jpg
Homework Equations
The Attempt at a Solution
Prove P(2) is true
then prove P(x) = P(x+1) is true, then it's true for all x
That's all I really from proof...