For the first, consider Newton's binomial expansion:
What happens if we let a=b=1?
(I'm not sure if this is in the right forum... since there is no forum that says "combinatorics")
I've just started combinatorics (basic) and just some beginner questions I can't do, if anyone could help with them it would be very much appreciated :lol: [Note: if it's possible please don't leave out any necessary steps or procedures I'm a beginner at these and pretty n00b haha]
1. Prove
2. Which are there more of among the natural numbers between and : Numbers that can be represented as a sum of a perfect square and a (positive) perfect cube or numbers that can not be?
3. Two of the squares of a checkerboard are painted yellow and the rest are painted green. Two color schemes are equivalent if one can be obtained from the other by applying a rotation in the plane of the board. How many inequivalent color schemes are possible?