I understand how to \"plug & chug\" with this formula: T(n)= floor(n*(n+2)*(2n+1

Question

I understand how to "plug & chug" with this formula: T(n)= floor(n*(n+2)*(2n+1)/8) Freidrich's formula, but I don't understand how each part (like why "n+2 and why divide by 8) directly relates to finding the total number of triangles in a triangle, such as a 10x10x10 triangle.

I understand that in this example, that n=10. Therefore, T(10)= floor(10*(10+2)*(2*10+1)/8)= 315.

So, my real ONE question is how does this formula work to actually show the total number of equilateral triangles inside one large equilateral triangle???????

Explanation / Answer

by induction we have to provethis.

since Freidrich already done that.

we can use.

else

take induction process.

prove that it istrue for n =1

then prove that n =k+1

then you are done !!

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects