311 351075623328 10Y759 r points en ometrie uence which has

3,-11 . 35-10756-23328 10Y759 r points) en ometrie uence which has as its first threes 2 -18.12 Which Show youm work using appropriate ormulas nEno 12 points) Find the sum of the infinite geometric se sum, show how you found it by the appropriate formula. ries, if it exists. If it does not exist, say (a) 4 (b) 212 8-6 Sn Find he rational mumber rpresentation f he epeating decimal. 1

Solution

a)_{n=1 to} 4(2/3)^n-1

_{n=1 to} 4(2/3)ⁿ/(2/3)

_{n=1 to} 6(2/3)ⁿ

first term a=6(2/3) , commonratio r =2/3, sum of infinate geometric series when |r|<1 is a/(1-r)

sum=6(2/3)/[1-(2/3)]

sum=6(2/3)/(1/3)

sum =12

b)_{n=1 to} (1/2)(4/3)ⁿ

common ration r =4/3>1

so series is divergent