Question

$1+\frac{3}{2}+\frac{5}{4}+\frac{7}{8}+.....nterms$

Answer 1

$1,\frac{3}{2},\frac{5}{4}+.............+n$

$S_n=\frac{a}{1-r}+\frac{dr}{(1-r{)}^2}$

$a=1,d=2,r=\frac{1}{2}$

$S_n=\frac{1}{1-\frac{1}{2}}+\frac{\left(2\right)\frac{1}{2}}{{(1-\frac{1}{2})}^2}$

$=\frac{1}{\frac{1}{2}}+\frac{1}{\frac{1}{4}}$

$=2+4$

$\therefore S_n=6$