用数学归纳法证明:1/n+1+1/n+2+1/n+3+…+1/2n>13/24(n≥2,n∈N*)
问题描述:
用数学归纳法证明:
+1 n+1
+1 n+2
+…+1 n+3
>1 2n
(n≥2,n∈N*) 13 24
答
证明:(1)当n=2时,12+1+12+2=1424,1424>1324命题成立.(2)假设当n=k时,1k+1+1k+2+1k+3+…+12k>1324成立当n=k+1时,1k+2+1k+3+…+12k+12k+1+12k+2=1k+1+1k+2+1k+3+…+12k+12k+1+12k+2−1k+1>1324+12k+1+12...