A math problem is like this: When Xiao Lin typed a manuscript, the ratio of typed to untapped was 5:3. If he typed another 140 words, the ratio of typed to untapped would become 4:1. How many words are there in this manuscript?

A math problem is like this: When Xiao Lin typed a manuscript, the ratio of typed to untapped was 5:3. If he typed another 140 words, the ratio of typed to untapped would become 4:1. How many words are there in this manuscript?

I played 5 / 8 and then 4 / 5
140 words is 4 / 5-5 / 8 of the manuscript
Therefore, the total number of manuscripts is 140 (4 / 5-5 / 8) = 800 words

There's a math problem like this
Of the 1000 numbers, only one is correct. You only have 500 chances to guess. What's the probability of getting the right number

（500*499*498*497*496）/(1000*999*998*997*996)=30814/996003

The original question is 1 / 1 * 2 * 3 + 1 / 2 * 3 * 4 +. + 1 / 98 * 99 * 100

1/1*2+1/2*3+1/3*4+.+1/98*99+1/99*100
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/98-1/99)+(1/99-1/100)
=1-1/2+1/2-1/3+1/3-1/4+...+1/98-1/99+1/99-1/100
=1-1/100
=99/100