Question

O limite da soma dos termos da PG (3/4, -1/2, 1/3, -2/9, ...) é

Answer 1

$LimS_n= \frac{a_1}{1-q} \\ \\ q= -\frac{1}{2\ } : \frac{3}{4}= -\frac{1}{2}* \frac{4}{3} =- \frac{4}{6}= -\frac{2}{3} \\ a_1= \frac{3}{4} \\ \\ LimS_n= \frac{a_1}{1-q} \\ \\ LimS_n= \frac{ \frac{3}{4} }{1-(- \frac{2}{3}) } \\ \\LimS_n= \frac{ \frac{3}{4} }{1+ \frac{2}{3} } \\ \\ LimS_n= \frac{ \frac{3}{4} }{\frac{3+2}{3} } \\ \\ LimS_n= \frac{ \frac{3}{4} }{\frac{5}{3} } \\ \\ LimS_n= \frac{3}{4}* \frac{3}{5} \\\boxed{ \boxed{LimS_n= \frac{9}{20}} }$