Prove by induction floor and ceiling

Question

I couldn't solve below question ... I was able to start the solution .. but I couldn't turn left side to be same as write side in the inductive step:

Neat Math · Answer

Hint: you only need to show
$$leftlceil frac{n+1}{m}rightrceil - leftlceil frac nm rightrceil = leftlfloor frac{n+m}{m} rightrfloor - leftlfloor frac{n+m-1}{m}rightrfloor$$
Now the LHS is either $0$ or $1$, usually $0$. So is the RHS.
When is LHS $1$? When is RHS $1$?

Prove by induction floor and ceiling

One Answer

Add your own answers!

Ask a Question