设Sk=1k+1+1k+2+…+12k，那么Sk+1=Sk+．

Question

设S_k=(1)/(k+1)+(1)/(k+2)+…+(1)/(2k)，那么S_k+1=S_k+______．

Answer 1

由S_k=(1)/(k+1)+(1)/(k+2)+…+(1)/(2k)，用K+1代替K
可得SK+1＝(1)/((k+1)+1)+(1)/((K+1)+2)+…+(1)/(2(K+1))
=(1)/(k+2)+(1)/(k+3)+…+(1)/(2k)+(1)/(2K+1)+(1)/(2K+2)
∴SK+1−SK＝(1)/(2K+1)+(1)/(2K+2)−(1)/(K+1)=(1)/(2k+1)−(1)/(2k+2)
∴SK+1＝SK+(1)/(2K+1)−(1)/(2K+2)
故答案为(1)/(2k+1)−(1)/(2k+2)