Answer
$S=3, \dfrac{9}{2},\dfrac{11}{2}, \dfrac{25}{4}, \dfrac{137}{2}$
Work Step by Step
Our aim is compute the first five partial sums for the given sequence.
$S_1=3; S_2=3+\dfrac{3}{2}=\dfrac{9}{2}; S_3=3+\dfrac{3}{2}+1=\dfrac{11}{2}; S_4=3+\dfrac{3}{2}+1+\dfrac{3}{4}=\dfrac{25}{4}; S_5=3+\dfrac{3}{2}+1+\dfrac{3}{4}+\dfrac{3}{5}=\dfrac{137}{20}$
Thus, our partial sums are:
$S=3, \dfrac{9}{2},\dfrac{11}{2}, \dfrac{25}{4}, \dfrac{137}{2}$
