Question

数学题 2乘4分之1加4乘6分之一加6乘8分之一......加2006乘2008分之一 的结果是？？？

Answer 1

解：
1/(2*4)+1/(4*6)+1/(6*8)+.....+1/(2006*2008)
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+......+1/2*(1/2006-1/2008)
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+....+1/2006-1/2008)
=1/2*(1/2-1/2008)
=1/2*(1003/2008)
=1003/4016
希望对你有帮助.

Answer 2

1/(2*4)+1/(4*6)+...+1/(2006*2008)
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+...+1/2*(1/2006-1/2008)
=1/2*[(1/2-1/4)+(1/4-1/6)+...+(1/2006-1/2008)]
=1/2*(1/2-1/2008)
=1003/4016

Answer 3

1/(2*4)+1/(4*6)+...+1/(2006*2008)
=1/2*(1/2-1/4)+1/2*(1/4-1/6)+...+1/2*(1/2006-1/2008)
=1/2*[(1/2-1/4)+(1/4-1/6)+...+(1/2006-1/2008)]
=1/2*(1/2-1/2008)
=1003/4016

Answer 4

=1/2（1/2-1/4+1/4-1/6+1/6-1/8+···+1/2004-1/2006+1/2006-1/2008）
=1/2（1/2-1/2008）
=1003/4016