Chapter 11 - Section 11.4 - Partial Sums of Arithmetic and Geometric Sequences - Exercise Set - Page 658: 25

$S_{7}=\dfrac{127}{21}$

Using $S_{n}=\dfrac{a_1(1-r^n)}{1-4}$, the sum of the first $ 7 $ terms of the sequence $ 3,\dfrac{3}{2},\dfrac{3}{4},... $ is \begin{array}{l} S_{7}=\dfrac{3\left(1-\left( \dfrac{1}{2} \right)^7\right)}{1-\dfrac{1}{2}}\\\\ S_{7}=\dfrac{3\left( \dfrac{127}{126} \right)}{\dfrac{1}{2}}\\\\ S_{7}=\dfrac{\dfrac{127}{42}}{\dfrac{1}{2}}\\\\ S_{7}=\dfrac{127}{21} .\end{array}