Question

2的三次方+4的三次方+6的三次方+98的三次方+…+100的三次方=

2的三次方+4的三次方+6的三次方+98的三次方+…+100的三次方= (过程详细)

Answer 1

1^3+2^3=1/4*4*9=1/4*2^2*3^2=9；

1^3+2^3+3^3=36=1/4*9*16=1/4*3^2*4^2
1^3+2^3+3^3+4^3=100=1/4*16*25=1/4*4^2*5^2
......
1^3+2^3+3^3+4^3+…+N^3=1/4*N^2*(N+1)^2
所以
2^3+4^3+6^3+......+98^3+100^3
=2^3+2^3*2^3+2^3*3^3+...+2^3*50^3
=2^3*(1^3+2^3+3^3+...+49^3+50^3)
=2^3*[1/4*50^2*(50+1)^2]
=8*(1/4)*2500*2601
=13005000

追问

能简便吗

追答

原式=(2^3)*(25*51)^
=8*25*25*51*51
=5000*51^
=13005000

Answer 2

13005000
private static int testMath()
{
int sum = 0;
for (int i = 0; i <= 100; i += 2)
{
sum += i * i * i;
}
return sum;
}