利用数学归纳法证明：对所有正整数 $n$，都有 $\big(\frac65\big)^n\geqslant1+\frac15n$。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

先检查n=1等号成立。归纳步骤乘正数6/5后，分离出目标下界与非负余项。

For $n=1$, both sides equal $6/5$, so the statement is true.

Assume that $(6/5)^k\ge1+k/5$ for some positive integer $k$. Multiplying by $6/5>0$,

Thus the statement holds for $k+1$. By mathematical induction,

for every positive integer $n$.