How do you find the sum of the infinite geometric series #8+6+9/2+27/8+...#?

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Answer 1 · 2017-10-26T16:45:20

#S_oo=32#

The sum of infinite GP is given by

#S_oo=a/(1-r)#

where

#a=#the first term

#r=#the common ratio

AND#" "|r|<1#" "if #" "S_oo" "#is to exist

we need to fin teh common ratio . We do this by

#r=(u_(n+1))/u_n#

#r=6/8=3/4#

#|r|<1" ":.S_oo" exists"#

# S_oo=8/(1-3/4)#

#S_oo=8/(1/4)=8xx4/1#

#S_oo=32#