I am not really sure I follow your question.
But it is well known that .
If then .
Hi,
I am helping my son do some maths homework. We have worked out that there are 204 squares on a chessboard, and we have worked out that this is relative to square numbers.
How can I express a formula tidily? Is there a function that is similar to Factorial but using addition? EG: x=n²+(n+1)²... (n+7)² simplified to a tidier function (where n = 8)?
The formulae for a chessboard is x=1²+2²+3²+4²+5²+6²+7²+8², so how can I use this using n? eg: something like x=(n²)! but without factorial and with the appropriate function?
Thanks, I'll try to re-phrase...
x=(n²)! (where n = 8)
expands to...
x=1²*2²*3²*4²*5²*6²*7²*8²
Can I use any function to do similar but using addition instead of multiplication eg...
x=1²+2²+3²+4²+5²+6²+7²+8²
so x = 204
Basically, a formula that works out how many squares a grid of any given size contains. EG: 8*8 grid has 204 possible squares within it (1², 2², 3², 4², 5², 6², 7², 8²)
Is this any clearer?