Sum of each of the following infinite series ?
1 Answer
Jan 20, 2018
Explanation:
#(a)#
#"this is a "color(blue)"geometric series"#
#"with "a=3#
#r=a_2/a_1=(-3(5/7))/3=-5/7#
#S_oo=a/(1-r)=3/(12/7)=7/4#
#(b)#
#"these are also geometric sequences"#
#sum_(k=1)^oo((4/9)^k-(1/8)^k)#
#=sum_(k=1)^oo(4/9)^k-sum_(k=1)^oo(1/8)^k#
#"with " a=4/9" and "r=4/9" and "a=1/8/r=1/8#
#S_oo=(4/9)/(1-4/9)-(1/8)/(1-1/8)#
#color(white)(S_oo)=4/5-1/7=23/35#
