Qiuyun TMUA Simulation Test Paper 1 · Question 19

$S_n$ is the sum of the first $n$ terms of $A_n$ . The first term $a_1=1$ and the sequence $\left\{\dfrac{S_n}{a_n}\right\}$ is an arithmetic sequence whose common difference is $\dfrac13$ .

Which of the following statements is true for all $n$ ?

\dfrac1{a_1}+\dfrac1{a_2}+\cdots+\dfrac1{a_n}<2

\dfrac1{a_1}+\dfrac1{a_2}+\cdots+\dfrac1{a_n}>2

\dfrac1{a_1}+\dfrac1{a_2}+\cdots+\dfrac1{a_n}<1

\dfrac1{a_1}+\dfrac1{a_2}+\cdots+\dfrac1{a_n}>1

ENone of the statements above is true.

examday

Qiuyun TMUA Simulation Test Paper 1 · Q19