Question

1/(k-1)•k=

1/2•1/k•1/（k+1）= 1/2（1/k - 1/（k+1））这是为啥
（1/2）•（1/k）•（1/（k+1））= 1/2（1/k - 1/（k+1））这是为啥

Answer 1

1/2*1/k*1/(k+1)=1/2*1/k[1--k/(k+1)]
=1/2*[1/k--1/(k+1)].
看懂了吗?先把1/(k+1)拆成两项的差1--k/(k+1),
然后用乘法分配律去乘 1/k*[1--k/(k+1)]=1/k--1/(k+1).