Question

Find the sum of the infinite series. 1.2 + 0.12 + 0.012 +

Answer 1

this is a geometric series where the ratio is 0.1.

The formula for a geoemtric series is \[\large \sum_{n=1}^{\infty}a_{1}r^{n-1}\]\[\large a_{1}= 1.2 \ ,\ r= 0.1\]
\[\large |r|<1 \ \text{ series converges}\]

Answer 2

And if the series converges, then you find the sum \[\large s_{n}= \frac{a}{1-r}\]

Answer 3

So first, does your series converge? If so, plug your values into the formula for the sum, and there you go.

Answer 4

how do you know if it converges?

Answer 5

if |r|<1

Answer 6

what is your ratio in this series?

Answer 7

0.1 right?

Answer 8

Yes, is |0.1| < 1?

Answer 9

yes

Answer 10

ok, so now we know the series converges.

To find the sum, plug a = 1.2 and r = 0.1 into

s(n) = (a)/ (1-r)

Answer 11

1.1?

Answer 12

\[\large \frac{1.2}{1-(0.1)}=\frac{1.2}{0.9}=?\]

Answer 13

1.3333

Answer 14

good job