1(7*7-1)+1(9*9-1)+1(11*11-1)+••••••1(99*99-1)求和

题目

1(7*7-1)+1(9*9-1)+1(11*11-1)+••••••1(99*99-1)求和

答案

简便计算
1(7*7-1)+1(9*9-1)+1(11*11-1)+••••••1(99*99-1)
=1/(7-1)(7+1)+1/(9-1)((+1)+1/(11-1)(11+1)+...+1/(99-1)(99+1)
=1/6x8+1/8x10+1/10x12+...+1/98x100
=1/2(1/6-1/8)+1/2(1/8-1/10)+1/2(1/10-1/12)+..+1/2(1/98-1/100)
=1/2(1/6-1/100)
=1/2(50/300-3/300)
=47/600