题目内容
求证:logn(n+1)＞log(n+1)(n+2),其中n∈N*且n＞1.
证明:欲证logn(n+1)＞log(n+1)(n+2)(其中n∈N*且n＞1),
只需证
,
只需证lgnlg(n+2)＜lg2(n+1),
而lgn·lg(n+2)＜
＜
［lg(n2+2n+1)］2=lg2(n+1)成立.
故logn(n+1)＞log(n+1)(n+2)成立.
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题目内容
求证:logn(n+1)＞log(n+1)(n+2),其中n∈N*且n＞1.
证明:欲证logn(n+1)＞log(n+1)(n+2)(其中n∈N*且n＞1),
只需证,
只需证lgnlg(n+2)＜lg2(n+1),
而lgn·lg(n+2)＜
＜［lg(n2+2n+1)］2=lg2(n+1)成立.
故logn(n+1)＞log(n+1)(n+2)成立.