Question

Determine the sum of each infinite geometric series, if it exists. a) t1=8, r=-1/4 b)t1=3, r=4/3

Answer 1

let, the first term=t1 and common ratio=r
so the sum of the infinite series,
=t1/(1-r) for r<1
=t1/(r-1) for r>1
now you evaluate for the two cases.

Answer 2

yup, i got for a) Sinfinity=6 1/2, and for b) Sinfinity=-9

Answer 3

but the back of the book says that b) has no sum... how do you know if it has a sum or not?

Answer 4

oh sorry. I made a mistake.
there will be no sum for infinite series with r>1
only sum for infinite series,
t1/(1-r) for |r|<1

Answer 5

oookkkayy..... but in b) r is more than 1....(r=4/3)

Answer 6

yes.
actually the sum for the second case diverges as the series is divergent. so we can nor calculate the infinite sum.

Answer 7

i think the back of the book is wrong... cause wouldn't it only have no sum if r is 0

Answer 8

if r=0 then the series will have only the first term.

Answer 9

the series is,
a, ar, ar^2, ar^3, ar^4,..............................