Question

各位数学高手,小妹有道题向各位请教,多谢了!!!!

1\1*2+1\2*3+1\3*4+^+1\99*100

Answer 1

1/1x2+1/2x3+1/3x4+.........1/98x99+1/99x100
=(1-1/2) + (1/2-1/3) + (1/3-1/4) + (1/98-1/99) + (1/99-1/100)
=1 - 1/100
=99/100

Answer 2

1\1*2+1\2*3+1\3*4+^+1\99*100
= (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + …… + (1/99 - 1/100)
= 1 - 1/100
= 99/100

Answer 3

对啊,就是列项求和法
恭喜楼上的得分快乐

Answer 4

1/a*(a+1)=1/a-1/(a+1)
所以原式=1-1/2+1/2-1/3……+1/99-1/100
=1-1/100=99/100

Answer 5

1\1*2+1\2*3+1\3*4+^+1\99*100
= (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + …… + (1/99 - 1/100)
= 1 - 1/100
= 99/100