analysis problem

Here it is underlying the original proof of the divergence of the harmonic series.

Define
$s_1=1>1/2$
$s_2=1/2$
$s_3=1/3+1/4>2(1/4)=1/2$
$s_4 =1/5+1/6+1/7+1/8>4(1/8)=1/2$
$s_5=1/9+\cdots+1/16>8(1/16)=1/2$

$<br /> s_n=(1/(2^{n-2}+1)+\cdots+1/2^{n-1}>(2^{n-1}-2^{n-2})1/2^{n-1}=1/2<br />$

$<br /> a_n=s_1+\cdots+s_{n}>n(1/2)<br />$

Now it follows that the harmonic series diverges, and also that your correct answer is b)!