How do you find the sum of the infinite geometric series given #3/2-3/4+3/8-...#?
1 Answer
Sep 14, 2017
Explanation:
#"the sum to n terms of a geometric sequence is"#
#•color(white)(x)S_n=(a(1-r^n))/(1-r)#
#"where a is the first term and r the common ratio"#
#"as "ntooo,r^nto0" and sum becomes"#
#S_oo=a/(1-r)color(white)(x);|r|<1#
#"here "a=3/2" and "d=-3/4xx3/2=-1/2#
#rArrS_oo=(3/2)/(1-(-1/2))=1#
