一个探索规律的数学问题

16 = 4*2^2

36 = 4*3^2

64 = 4*4^2

100 = 4*5^2

144 = 4*6^2

-(编号100)...4 * 100次方2 = 40000

5 = 2 + 3

10 = 5 + 5

17 = 10 + 7

26 = 17 + 9 .............a(n) = a(n-1) + (2n-1)

a(1) = 2

a(2) = 2 + (2*2 - 1)

a(3)= 2+(2 * 2-1)+(2 * 3-1)

a(4)= 2+(2 * 2-1)+(2 * 3-1)+(2 * 4-1)

....

a(50) = 2 + 2*(2 + 3 + 4 +)....+ 50) - (50 - 1)

= 2*(1 + 2 + 3 + ....+ 50) - 50 + 1

= 2*[(1 + 50)*50/2] - 50 + 1

= 50*51 - 50 + 1

= 50*50 + 1

= 2501