求证不等式mβ{(1+β)^m/[(1+β)^m-1]}-1

Question

求证 不等式 mβ{ (1+β)^m/[(1+β)^m-1] } - 1 < β×m
mβ{ (1+β)^m/[(1+β)^m-1] } - 1 < β×m,其中 m为不为零的自然数,β为小于1大于零的百分数

Answer 1

证：先将mβ{ (1+β)^m/[(1+β)^m-1] }-1