1*100+2*99+3*98+4*97+(省略号）+50*51

题目

1*100+2*99+3*98+4*97+(省略号）+50*51

答案

n(101-n)=101n-n^2
所以原式=101*(1+2+3+……50)-(1^2+2^2+3^2+……+50^2)
=101*50*51/2-50*(50+1)(2*50+1)/6
=50*51*(101/2-101/6)
=50*51*101/3
=85850