Question

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+1/10*11+1/11*12+1/12*13+1/13*14+1/14*15=?

Answer 1

1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
……
依此类推，最后相加得
1-1/15=14/15

Answer 2

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+1/10*11+1/11*12+1/12*13+1/13*14+1/14*15
=（1/1-1/2）+（1/2-1/3）+……+（1/14-1/15）
=1/1-1/2+1/2-1/3+……+1/14-1/15
=1-1/15
=14/15

Answer 3

14/15

Answer 4

？？？1/1*2
2乘的是分母还是1/1？？
要都是乘以分母的话就是14/15
要是乘以前面的分式那就是。。。。就是LZ你变态！！！

Answer 5

14/15

Answer 6

1/N(N+1)=1/N-1/(N+1)

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+1/10*11+1/11*12+1/12*13+1/13*14+1/14*15
=1-1/2+1/2-1/3+1/3-1/4+......+1/14-1/15
=1-1/15=14/15懂了吗？