计算,1/2x4+1/4x6+1/6x8+.+1/48x50=?,1/2+1/6+1/12+1/20+1/30+1/42

计算,
1/2x4+1/4x6+1/6x8+.+1/48x50
=1/2×（1/2-1/4+1/4-1/6+1/6-1/8+……+1/48-1/50）
=1/2×（1/2-1/50）
=1/2×12/25
=6/25,
1/2+1/6+1/12+1/20+1/30+1/42
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7

答：两道题目考查的都是分数的裂项：
1/(2x4)+1/(4x6)+1/(6x8)+......+1/(48x50)
=(1/2)x(1/2-1/4+1/4-1/6+1/6-1/8+....+1/48-1/50)
=(1/2)x(1/2-1/50)
=1/4-1/100
=6/25
1/2+1/6+1/12+1/20+1/30+1/42
=1/(1x2)+1/(2x3)+1/(3x4)+......+1/(6x7)
=1-1/2+1/2-1/3+...+1/6-1/7
=1-1/7
=6/7