设P（x）=1/(k+1)+1/(k+2)+.+1/2k,则P(x+1)的值是?
问题描述：
设P（x）=1/(k+1)+1/(k+2)+.+1/2k,则P(x+1)的值是?
答案是p（k）+1/(2k+1)-2/(2k+2)请写出解题过程,谢谢~
答
P（k）=1/(k+1)+1/(k+2)+.+1/2k
P(k+1)=1/(k+2)+1/(k+3)+.+1/(2k+1)+1/(2k+2)
=P(k)-1/(k+1)+1/(2k+1)+1/(2k+2)
=P(K)+1/(2k+1)-1/(2k+2)