Question

2×1/4 4×1/6 6×1/8加上省略号,加上48×1/50。

Answer 1

1/2*4+1/4*6+1/6*8+....1/48*50 =1/2*(1/2-1/4)+1/2*(1/4-1/6)+1/2*(1/6-1/8)+......+1/2*(1/48-1/50) =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

Answer 2

裂项法
1/2×1/44×1/6+1/6×1/8+……+1/48×1/50
=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