What do you think the appropriate limit is of this sequence?

Question

0.7, 0.72, 0.727, 0.7272,...

The answer my textbook gives is 27/99. I have no idea how they got that answer. How do I solve this question?

Answer 1

.72*10^0 +.72*10^-2 + .72*10^-4 +.72*10^6

geometric sequence
each term is r = 10^-2 times the preceding term
sum of infinite series
= a/(1-r) = .72/(1-10^-2)
= .72/(1-.01)
= .72/(0.99)
= 72/99
try dividing 72 by 99 on your calculator :)