Originally Posted by

**nerazzurri10** I have an assignment which I am quite stuck on. The question is the following:

function f: N to N is defined recursivly:

f(k+1)=(k+1)*f(k) for each k in N. f(0)=1.

Now I have to prove by induction:

1* f (1) + 2 * f (2) + 3* f (3) +....+n * f (n) = f (n +1) -1

I have made two steps:

1. proved that the equation is true for n=1.

2. I assume that the equation is true for n.

Now I have to prove the equation for n+1.

Now the equation is:

1* f (1) + 2 * f (2) + 3* f (3) +....+n * f (n) + (n+1)*f(n+1) = f (n +2) -1

I have used the induction assumption (number 2 in my steps) to place:

f (n +1)-1

insted of:

1* f (1) + 2 * f (2) + 3* f (3) +....+n * f (n)

So now I got:

f(n+1)-1 + (n+1)*f(n+1)=f(n+2)-1