解法一:
2+6+12+20+30+.99*100
=1x2 + 2x3 + 3x4 +...+ 99x100
=1(1+1) + 2(2+1) +3(3+1) +...+ 99(99+1)
=(1^2 + 2^2 +3^2+...+99^2) + (1+2+3+...+99)
=99(99+1)(99x2+1)/6 + (1+99)99/2
=333300
解法二:
原式
=2 [C(2,2) + C(2,3) + C(2,4) +...+C(2,100)] (注:组合数)
=2 * C(3,101)
=333300