Math Is Fun Forum

Sure you wanted to go into that in the other thread? I mean about the artificial intelligence work. You are correct and all but young people should not be exposed to different viewpoints. It will confuse them.

Hello:

I am pleased to meet you. You do not have to limit yourself to the use of Geogebra, you are M capable too.

It looks like the right answer.

Did I guess the two questions?

For n = 1...3

Let

The equations are

I used the arithmetic nth term formula.

From what is above.

Hello;

I'm using an algorithmic method that he showed me. I don't know what is wrong with your method. M says, use methods that work.

Hello administrator;

The problem is from another site and is active please cover it up.

Hello Agnishom;

bobbym tells me you are learning M:) Then this is for you.

I computed the answer and used the number of terms in the generating function as a cute test

ans4 = Tuples[{{thk, thn}, {a, b, c, d, e, f}, {a, b, c, d, e, f}, {a,
      b, c, d, e, f}, {a, b, c, d, e, f}}];
ans4 = Union[Sort[#] & /@ ans4];
Length[ans4]
List @@ Expand[(thk + thn) (a + b + c + d + e + f)^4] // Length

252

ans3 = Tuples[{{thk, thn}, {a, b, c, d, e, f}, {a, b, c, d, e, f}, {a,
      b, c, d, e, f}}];
ans3 = Union[Sort[#] & /@ ans3];
Length[ans3]
List @@ Expand[(thk + thn) (a + b + c + d + e + f)^3] // Length

112

ans2 = Tuples[{{thk, thn}, {a, b, c, d, e, f}, {a, b, c, d, e, f}}];
ans2 = Union[Sort[#] & /@ ans2];
Length[ans2]
List @@ Expand[(thk + thn) (a + b + c + d + e + f)^2] // Length

42

ans1 = Tuples[{{thk, thn}, {a, b, c, d, e, f}}];
ans1 = Union[Sort[#] & /@ ans1];
Length[ans1]
List @@ Expand[(thk + thn) (a + b + c + d + e + f)^1] // Length

12

ans0 = Tuples[{{thk, thn}}];
ans0 = Union[Sort[#] & /@ ans0];
Length[ans0]
List @@ Expand[(thk + thn) (a + b + c + d + e + f)^0] // Length

2

252 + 112 + 42 + 12 + 2 = 420

That post earlier about .999999... it does sound like that guy you told me about:(

Hello:

It is the most basic attribute we have. M knows that.

Hello:

The best way is to work like the M would, experimentally! Although he does seem to have borrowed the idea from Doctor Z as he calls him.

Form a difference table:

{3,6,10,15,21,28,36,45,55}

{3,4,5,6,7,8,9,10}

{1,1,1,1,1,1,1}

The third row is constant so it is a cubic

Using bobbym's idea in

http://www.mathisfunforum.com/viewtopic … 18#p285718

which is the binomial in the question. You should use induction to show that the formula is correct.