证明:1+1/2+1/3+1/4+…1/2n−1>n/2(n∈N*),假设n=k时成立,当n=k+1时,左端增加的项数是_.
问题描述:
证明:1+
+1 2
+1 3
+…1 4
>1 2n−1
(n∈N*),假设n=k时成立,当n=k+1时,左端增加的项数是______. n 2
答
当n=k时不等式为:1+
+1 2
+1 3
+…+1 4
>1 2k−1
成立k 2
当n=k+1时不等式左边为1+
+1 2
+1 3
+…+1 4
+1 2k−1
+1 2k
,1 2k+1
则左边增加2k+2-2k=2项.
故答案为:2.