1/20+1/30+1/42+……+1/9900等于多少?

1/20+1/30+1/42+……+1/9900等于多少?
1/20+1/30+1/42+……+1/9900等于多少?

1/20+1/30+1/42+……+1/9900等于多少?
1/20+1/30+1/42+……+1/9900
=1/(4×5)+1/(5×6)+1/(6×7)+……+1/(99×100)
=(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+……(1/99-1/100)
=1/4-1/5+1/5-1/6+1/6-1/7+……+1/99-1/100
=1/4-1/100
=25/100-1/100
=24/100
=6/25

1/20+1/30+1/42+……+1/9900
=1/4-1/5+1/5-1/6+1/6-1/7+……+1/99-1/100
=1/4-1/100
=6/25

1/20+1/30+1/42+……+1/9900
=1/4*5+1/5*6+1/6*7+……+1/99*100
=1/4-1/5+1/5-1/6+1/6-1/7+……+1/99-1/100
=1/4-1/100
=6/25