Proof by Induction

what are you actually trying to prove? The sum of the left side equals the right side?

>>205982
Proof by induction is basically restating that equation with every n set to (n+1), then mangling the left side until it has the same form of the right side. It's discrete math.

>>205984
Sorry, mangling the right side until it has the form of the left side.

its been a while since I've done this, but aren't both sides of the equation double the simple formula of the sum of n and the sum of n^2?

>>205988
it's the product of two consecutive integers: (2)(3), (4)(5), etc.

>>205980
n=1

>>205980
I don't know wtf is going on but the premise of OP's is wrong as shit.

For n = 2,

n*(n + 1) = 2*3 = 6

and n*(n + 1)*(n + 2) = 2*3*4 = 24

There's nothing to prove by induction, it's almost always wrong. Unless you just want to solve the equation, then that's another story.

Please precise, OP.

>>205995
0 and -1 are possible solutions too, although -1 may not be if n is in N

and there are no other solutions

>>206374
(because obviously, either n(n+1) != 0 and then we can divide both sides of the equation by n(n+1) and get 1=(n+2)/3 so n=1, or n(n+1) = 0 and then we get n=0 or n=-1)