Question

求数学高手解两道数学题

1.计算(1×100+2×99+3×98……+51×50)×2= 2.(1×2+2×3)(1/1×2+1/2×3)+(2×3+3×4)(1/2×3+1/2×3+3×4)+……+(19×20+20×21)(1/19×20+1/20×21)=

Answer 1

第题:[1×100+2×(100-1)+3×(100-2)+……+51×(100-50)]×2
=(1×100+2×100-2×1+3×100-3×2+……+51×100-51×50)×2
=[(1+2+…51)×100-(2×1+3×2+4×3+…+51×50)]×2
=[1326×100-(2×1+3×2+4×3+…+51×50)]×2
=(132600-44200)×2
=98400×2
=196800
其"1+2+3…+51"用梯形公式晓吧?
(首项+末项)×项数÷2
另外"2×1+3×2+4×3+…+51×50"用公式晓?
我问才晓,呵呵,惭愧啊!
N×(N+1)×(N+2)除三