gaokao 2025 Q16

gaokao · China · national-I 15 marks Arithmetic Sequences and Series Prove a Sequence is Arithmetic

Let the sequence $\{a_n\}$ satisfy $a_1 = 3$, $\frac{a_{n+1}}{n} = \frac{a_n}{n+1} + \frac{1}{n(n+1)}$.
(1) Prove that $\{na_n\}$ is an arithmetic sequence.
(2) Let $f(x) = a_1 x + a_2 x^2 + \cdots + a_m x^m$. Find $f'(-2)$.

Let the sequence $\{a_n\}$ satisfy $a_1 = 3$, $\frac{a_{n+1}}{n} = \frac{a_n}{n+1} + \frac{1}{n(n+1)}$.\\
(1) Prove that $\{na_n\}$ is an arithmetic sequence.\\
(2) Let $f(x) = a_1 x + a_2 x^2 + \cdots + a_m x^m$. Find $f'(-2)$.

Paper Questions

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