從題上可看出,“三角形數(shù)”的規(guī)律為 An = n(n+1)/2
而對應(yīng)的“正方形數(shù)”的規(guī)律為 Bn = n²
因為,An = n(n+1)/2,A(n-1) = (n-1)n/2
兩者之和 An+A(n-1) = n(n+1)/2+(n-1)n/2 = n²/2+n/2+n²/2-n/2 = n² = Bn
即所謂的,“正方形數(shù)”都可以看作兩個相鄰“三角形數(shù)”之和.
當(dāng) Bn = 2500 時,則 n = √2500 = 50
則 An = 50*51/2 = 1275,A(n-1) = 49*50/2 = 1225
所以,2500 = 1225 + 1275